Assertion : The set of all real numbers a such that a² + 2a, 2a + 3 and a² + 3a + 8 are the sides of a triangle is (5, ).
Reason : Since in a triangle sum of two sides is greater than the other and also sides are always positive.

Assertion : The distance of the orthocentre of ΔABC from its vertex A is 2R cos A
Reason : Orthocentre is the point of intersection of altitudes drawn from opposite vertex to the sides of triangle.

Assertion : The orthocentre of the given triangle is coincident with the in-centre of the pedal triangle of the given triangle.
Reason : Pedal triangle is the ex-central triangle of the given triangle.

The angles of a triangle ABC satisfy the relations 3B –C = 30º and A + 2B = 120º. If the perimeter of  the triangle is 2 (), then the largest side is C = 2 + 2.
Reason : Largest side in a triangle is the side opposite to the largest angle.

Assertion: In any triangle a cos A + b cos B + c cos 
Reason: In any trianglesinsinsin  

Assertion : If in a triangle sin²A + sin²B + sin²C = 2 then one of the angles must be 90º.
Reason : In any triangle sin²A + sin²B + sin² C = 2 + 2 cos A cos B cos C

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

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  x side2. Find the length of one side of the triangle in which  you have three circle is given with radius 1 unit.

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.

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-

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-

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 :

In a ΔABC, 2ac sin