Maths-

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Question

Assertion : If in a triangle tan A : tan B : tan C = 1 : 2 : 3 then A = 45º
Reason : If p : q : r = 1 : 2 : 3 then p = 1

If both (A) and (R) are true, and (R) is the correct explanation of (A).
If both (A) and (R) are true but (R) is not the correct explanation of (A).
If (A) is true but (R) is false.
If (A) is false but (R) is true.

The correct answer is: If (A) is true but (R) is false.

The reason R is obviously wrong. To test the assertion , we have
tan A = k, tan B = 2k, tan C = 3k
On putting these in the triangle identity
tan A + tan B + tan C = tan A tan B tan C
We get k + 2k + 3k = k. 2k. 3k
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 6 straight k equals 6 straight k cubed end cell row cell not stretchy rightwards double arrow straight k equals 0 comma 1 comma negative 1 end cell end table$
k = 0 and k = –1 are not possible.
(If k = 0 all angles become zero. If k = –1 all angles become obtuse).
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow straight k equals 1 not stretchy rightwards double arrow tan invisible function application straight A equals 1 end cell row cell not stretchy rightwards double arrow straight A equals 45 to the power of ring operator end cell end table$
Hence the assertion is true.

In any equilateral Δ, three circles of radii one are touching to the sides given as in the figure then area of the Δ

In this question, we have to find the area of the triangle, The formula of area of equilateral triangle is $fraction numerator square root of 3 over denominator 4 end fraction$ x side2. Find the length of one side of the triangle in which you have three circle is given with radius 1 unit.

In any equilateral Δ, three circles of radii one are touching to the sides given as in the figure then area of the Δ

Maths-General

General

Maths-

Which of the following pieces of data does not uniquely determine an acute angled triangle ABC (R being the radius of the circumcircle) -

In this question, the which is not uniquely determine an acute angled triangle. If we know a, sin A , R, then we can get the ratio b/sin B or c/sin(A+B) only. We cannot determine the values of b, c, sin B, sin C separately.

Which of the following pieces of data does not uniquely determine an acute angled triangle ABC (R being the radius of the circumcircle) -

Maths-General

General

Maths-

Let A₀ A₁ A₂ A₃ A₄ A₅ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A₀A₁, A₀A₂, and A₀A₄ is -

Maths-General

General

maths-

In a triangle ABC, a : b : c = 4 : 5 : 6 . The ratio of the radius of the circumcircle to that of the incircle is-

maths-General

General

Maths-

A regular polygon of nine sides, each of length 2 is inscribed in a circle. The radius of the circle is -

Maths-General

General

maths-

In any ΔABC having sides a, b, c opposite to angles A, B, C respectively, then-

maths-General

General

maths-

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then A : B : C is-

maths-General

General

maths-

If the angles of a triangle are in ratio 4 : 1 : 1 then the ratio of the longest side and perimeter of triangle is :

maths-General

General

maths-

In a ΔABC, 2ac sin $open parentheses fraction numerator straight A minus straight B plus straight C over denominator 2 end fraction close parentheses equals$

maths-General

General

maths-

In a triangle PQR, $straight angle R equals pi over 2$ .If tan $open parentheses straight P over 2 close parentheses$ and tan $open parentheses Q over 2 close parentheses$ are the roots of the equation ax² + bx + c = 0(a ≠ 0), then

maths-General

General

maths-

In a triangle ABC, a : b : c = 4 : 5 : 6, then the ratio of circum-radius to that of the in-radius is-

maths-General

General

maths-

In a ΔABC, let $straight angle C equals pi over 2$ . If r and R are the inradius and the circumradius respectively of the triangle then 2(r + R) is equal to -

maths-General

General

maths-

In-circle of radius 4 cm of a triangle ABC touches the side BC at D. If BD = 6cm., DC = 8 cm, then the area of the triangle ABC is-

maths-General

General

maths-

In a ΔABC, $r subscript 1 less than r subscript 2 less than r subscript 3$ , then

maths-General

General

maths-

ΔABC and ΔDEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual notations). a, b, c, and d, e, f satisfy the relation $square root of a plus b plus c end root square root of d plus straight e plus straight f end root equals square root of ad plus square root of be plus square root of cf$ then -

maths-General

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Assertion : If in a triangle tan A : tan B : tan C = 1 : 2 : 3 then A = 45ºReason : If p : q : r = 1 : 2 : 3 then p = 1

If both (A) and (R) are true, and (R) is the correct explanation of (A).If both (A) and (R) are true but (R) is not the correct explanation of (A).If (A) is true but (R) is false.If (A) is false but (R) is true.

The correct answer is: If (A) is true but (R) is false.

Related Questions to study

In any equilateral Δ, three circles of radii one are touching to the sides given as in the figure then area of the Δ

In any equilateral Δ, three circles of radii one are touching to the sides given as in the figure then area of the Δ

Which of the following pieces of data does not uniquely determine an acute angled triangle ABC (R being the radius of the circumcircle) -

Which of the following pieces of data does not uniquely determine an acute angled triangle ABC (R being the radius of the circumcircle) -

Let A0 A1 A2 A3 A4 A5 be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A0A1, A0A2, and A0A4 is -

Let A0 A1 A2 A3 A4 A5 be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A0A1, A0A2, and A0A4 is -

In a triangle ABC, a : b : c = 4 : 5 : 6 . The ratio of the radius of the circumcircle to that of the incircle is-

In a triangle ABC, a : b : c = 4 : 5 : 6 . The ratio of the radius of the circumcircle to that of the incircle is-

A regular polygon of nine sides, each of length 2 is inscribed in a circle. The radius of the circle is -

A regular polygon of nine sides, each of length 2 is inscribed in a circle. The radius of the circle is -

In any ΔABC having sides a, b, c opposite to angles A, B, C respectively, then-

In any ΔABC having sides a, b, c opposite to angles A, B, C respectively, then-

If the sides a, b, c of a triangle are such that a : b : c : : 1 : : 2, then A : B : C is-

If the sides a, b, c of a triangle are such that a : b : c : : 1 : : 2, then A : B : C is-

If the angles of a triangle are in ratio 4 : 1 : 1 then the ratio of the longest side and perimeter of triangle is :

If the angles of a triangle are in ratio 4 : 1 : 1 then the ratio of the longest side and perimeter of triangle is :

In a ΔABC, 2ac sin

In a ΔABC, 2ac sin

In a triangle PQR, .If tan and tan are the roots of the equation ax2 + bx + c = 0(a ≠ 0), then

In a triangle PQR, .If tan and tan are the roots of the equation ax2 + bx + c = 0(a ≠ 0), then

In a triangle ABC, a : b : c = 4 : 5 : 6, then the ratio of circum-radius to that of the in-radius is-

In a triangle ABC, a : b : c = 4 : 5 : 6, then the ratio of circum-radius to that of the in-radius is-

In a ΔABC, let . If r and R are the inradius and the circumradius respectively of the triangle then 2(r + R) is equal to -

In a ΔABC, let . If r and R are the inradius and the circumradius respectively of the triangle then 2(r + R) is equal to -

In-circle of radius 4 cm of a triangle ABC touches the side BC at D. If BD = 6cm., DC = 8 cm, then the area of the triangle ABC is-

In-circle of radius 4 cm of a triangle ABC touches the side BC at D. If BD = 6cm., DC = 8 cm, then the area of the triangle ABC is-

In a ΔABC, , then

In a ΔABC, , then

ΔABC and ΔDEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual notations). a, b, c, and d, e, f satisfy the relation then -

ΔABC and ΔDEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual notations). a, b, c, and d, e, f satisfy the relation then -

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Assertion : If in a triangle tan A : tan B : tan C = 1 : 2 : 3 then A = 45º
Reason : If p : q : r = 1 : 2 : 3 then p = 1

If both (A) and (R) are true, and (R) is the correct explanation of (A).
If both (A) and (R) are true but (R) is not the correct explanation of (A).
If (A) is true but (R) is false.
If (A) is false but (R) is true.

Let A₀ A₁ A₂ A₃ A₄ A₅ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A₀A₁, A₀A₂, and A₀A₄ is -

Let A₀ A₁ A₂ A₃ A₄ A₅ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A₀A₁, A₀A₂, and A₀A₄ is -

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then A : B : C is-

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then A : B : C is-

In a ΔABC, 2ac sin $open parentheses fraction numerator straight A minus straight B plus straight C over denominator 2 end fraction close parentheses equals$

In a ΔABC, 2ac sin $open parentheses fraction numerator straight A minus straight B plus straight C over denominator 2 end fraction close parentheses equals$

In a triangle PQR, $straight angle R equals pi over 2$ .If tan $open parentheses straight P over 2 close parentheses$ and tan $open parentheses Q over 2 close parentheses$ are the roots of the equation ax² + bx + c = 0(a ≠ 0), then

In a triangle PQR, $straight angle R equals pi over 2$ .If tan $open parentheses straight P over 2 close parentheses$ and tan $open parentheses Q over 2 close parentheses$ are the roots of the equation ax² + bx + c = 0(a ≠ 0), then

In a ΔABC, let $straight angle C equals pi over 2$ . If r and R are the inradius and the circumradius respectively of the triangle then 2(r + R) is equal to -

In a ΔABC, let $straight angle C equals pi over 2$ . If r and R are the inradius and the circumradius respectively of the triangle then 2(r + R) is equal to -

In a ΔABC, $r subscript 1 less than r subscript 2 less than r subscript 3$ , then

In a ΔABC, $r subscript 1 less than r subscript 2 less than r subscript 3$ , then