MCQ (Previous Year Questions) - Triangle (Competition Level 1) - JEE MCQ

The sides of a triangle are sin α, cos α and   for some  Then the greatest angle of the triangle is-

In a triangle ABC, let ∠c = π/2 If r is the  in-radius and R is the circumradius of the triangle ABC, then 2(r + R) equals -

[AIEEE-2005]

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is -          

[AIEEE-2010]

ABCD is a trapezium such that AB and CD are parallel and , BC = p and CD = q, then AB is equal to :

[JEE-MAIN 2013]

The radii r₁, r₂, r₃ of escribed circles of a triangle ABC are in harmonic progression. If its area is 24 sq. cm and its perimeter is 24 cm, find the lengths of its sides.

[REE 99, 6]

(a) In a triangle ABC, Let ∠C = π/2 . If 'r' is the inradius and 'R' is the circumradius of the triangle, then 2(r + R) is equal to [JEE 2000 (Scr.), 1 + 1]

(b) In a triangle ABC, 2 ac sin 1/2 (A – B + C) =

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

[JEE 2002 (Scr.), 3]

The ratio of the sides of a triangle ABC is 1 : √3 : 2. The ratio A : B : C is

[JEE 2004, (Scr.)]

 In ΔABC, a, b, c are the lengths of its sides and A, B, C are the angles of triangle ABC. The correct relation is

 Circles with radii 3, 4 and 5 touch each other externally if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the points of contact.

[JEE 2005 (Mains)]

Given an isosceles triangle, whose one angle is 120º and radius of its incircle is √3 . Then the area of triangle in sq. units is

[JEE 2006, 3]

Internal bisector of ∠A of a triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent side of ΔABC then

 [JEE 2006, 5]

Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2 2 and angle B = 30º. The absolute value of the difference between the areas of these triangles is

[JEE 2009, 5]

In a triangle ABC with fixed base BC, the vertex A moves such that cosB + cosC = 4 sin ²A/2. If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then

[JEE 2009]

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression 

Let ABC be a triangle such that ∠ACB = π/6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x² + x + 1, b = x² – 1 and c = 2x + 1 is (are)

Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of t he t riang l e i s 15 √3 . If ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r² is equal to

[JEE 2010]

Let PQR be a triangle of area D with a = 2, b =7/2 and c =5/2  where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then