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Maths-

General

Easy

Question

If a right-angled ABC of maximum area is inscribed within a circle of radius R, then-

 = 2R²
$\frac{1}{r_{1}}$ + $\frac{1}{r_{2}}$ + $\frac{1}{r_{3}}$ = $\frac{\sqrt{2} + 1}{R}$
r = ( $\sqrt{2}$ – 1) R
s = (1 + $\sqrt{2}$ )R

The correct answer is: $fraction numerator 1 over denominator r subscript 1 end subscript end fraction$ + $fraction numerator 1 over denominator r subscript 2 end subscript end fraction$ + $fraction numerator 1 over denominator r subscript 3 end subscript end fraction$ = $fraction numerator square root of 2 plus 1 over denominator R end fraction$

For a right-angled triangle inscribed in a circle of radius R, the length of the hypotenuse is 2R.  the area is maximum when the triangle is isosceles with each side = $square root of 2$ R.

 s = $fraction numerator 1 over denominator 2 end fraction$ (2 $square root of 2$ + 2) R = ( $square root of 2$ + 1)R
 = $fraction numerator 1 over denominator 2 end fraction$ $square root of 2$ R. $square root of 2$ R = R²  $fraction numerator 1 over denominator r end fraction$ = $fraction numerator left parenthesis square root of 2 plus 1 right parenthesis over denominator R end fraction$
$fraction numerator 1 over denominator r subscript 1 end subscript end fraction$ + $fraction numerator 1 over denominator r subscript 2 end subscript end fraction$ + $fraction numerator 1 over denominator r subscript 3 end subscript end fraction$ = $fraction numerator s minus a over denominator capital delta end fraction$ + $fraction numerator s minus b over denominator capital delta end fraction$ + $fraction numerator s minus c over denominator capital delta end fraction$
= $fraction numerator s over denominator capital delta end fraction$ = $fraction numerator 1 over denominator r end fraction$ = $fraction numerator square root of 2 plus 1 over denominator R end fraction$

Related Questions to study

The motion of a particle along a straight line is described by equation :
$x equals 8 plus 12 t minus t to the power of 3 end exponent$
Where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero, is

The motion of a particle along a straight line is described by equation :
$x equals 8 plus 12 t minus t to the power of 3 end exponent$
Where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero, is

Physics-General

A ball is thrown vertically upwards with a velocity of $25 blank m s to the power of negative 1 end exponent$ from the top of a tower of height 30 m. How long will it travel before it hits ground?

A ball is thrown vertically upwards with a velocity of $25 blank m s to the power of negative 1 end exponent$ from the top of a tower of height 30 m. How long will it travel before it hits ground?

Physics-General

In a triangle ABC, let ÐC = $fraction numerator pi over denominator 2 end fraction$ . If r is the in radius and R is the circumradius of the triangle, then 2(r + R) is equal to -

In a triangle ABC, let ÐC = $fraction numerator pi over denominator 2 end fraction$ . If r is the in radius and R is the circumradius of the triangle, then 2(r + R) is equal to -

parallel

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 -

Let L sin q = 10 + log sin q. The number of triangles ABC such that log b + 10 = log c + L sin B is-

Let L sin q = 10 + log sin q. The number of triangles ABC such that log b + 10 = log c + L sin B is-

If for a DABC, cot A. cot B. cot C > 0 then the triangle is-

If for a DABC, cot A. cot B. cot C > 0 then the triangle is-

parallel

In a triangle PQR as shown in figure given that x : y : z :: 2 : 3 : 6, then the value of ÐQPR is -

In a triangle PQR as shown in figure given that x : y : z :: 2 : 3 : 6, then the value of ÐQPR is -
Maths-General

The in-radius of the triangle formed by the axes and the line 4x + 3y – 12 = 0 is -

The in-radius of the triangle formed by the axes and the line 4x + 3y – 12 = 0 is -

In a  ABC if r1 = 2r2 = 3r3, then -

In a  ABC if r1 = 2r2 = 3r3, then -

parallel

The area of a circle is A1 and the area of a regular pentagon inscribed in the circle is A2. Then A1 : A2 is -

The area of a circle is A1 and the area of a regular pentagon inscribed in the circle is A2. Then A1 : A2 is -

If A, A1, A2, A3 be the area of the in-circle and ex-circles, then $fraction numerator 1 over denominator square root of A subscript 1 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 2 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 3 end subscript end root end fraction$ is equal to-

If A, A1, A2, A3 be the area of the in-circle and ex-circles, then $fraction numerator 1 over denominator square root of A subscript 1 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 2 end subscript end root end fraction plus fraction numerator 1 over denominator square root of A subscript 3 end subscript end root end fraction$ is equal to-

If $fraction numerator r over denominator r subscript 1 end subscript end fraction$ = $fraction numerator r subscript 2 end subscript over denominator r subscript 3 end subscript end fraction$ , then -

If $fraction numerator r over denominator r subscript 1 end subscript end fraction$ = $fraction numerator r subscript 2 end subscript over denominator r subscript 3 end subscript end fraction$ , then -

parallel

16R2 r r1 r2 r3 =

16R2 r r1 r2 r3 =

If a , b, c are in A.P., then r1, r2, r3 are in

If a , b, c are in A.P., then r1, r2, r3 are in

If the sides be a, b, c then (r1–r) (r2+ r3) =

If the sides be a, b, c then (r1–r) (r2+ r3) =

parallel

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