Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Advanced 2010Paper 2

Exam: JEE Advanced
Year: 2010
Paper: Paper 2
Subject: Mathematics
Chapter: Properties of Triangles

JEE Advanced 2010 · Paper 2 · Mathematics · Properties of Triangles

Consider a triangle A B C and let a, b and c denote the lengths of...

Consider a triangle

A B C

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 the triangle is

15 \sqrt{3}

. If

\angle A C B

is obtuse and if

r

denotes the radius of the incircle of the triangle, then

r^2

is equal to

Correct answer

0

Step-by-step solution

\sin C=\frac{\sqrt{3}}{2}

and C is given to be obtuse

\begin{aligned}& \Rightarrow \quad C=\frac{2 \pi}{3}=\sqrt{a^2+b^2-2 a b \cos C}\\ & =\sqrt{6^2+10^2-2 \times 6 \times 10 \times \cos \frac{2 \pi}{3}}=14 \\ & \therefore \quad r=\frac{\Delta}{s} \Rightarrowr^2=\frac{225 \times 3}{\left(\frac{6+10+14}{2}\right)^2}=3 \end{aligned}

$

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In a triangle ABC, BC=7, AC=8, AB=α ∈ N and A=(2)/(3) . If 49 (3 C)+42= m n , where (m… JEE Main 2024 Consider an obtuse angled triangle ABC in which the difference between the largest and… JEE Advanced 2023 Consider an obtuse angled triangle ABC in which the difference between the largest and… JEE Advanced 2023 For a triangle ABC , the value of 2A + 2B + 2C is least. If its inradius is 3 and… JEE Main 2023 Let ABC be the triangle with AB = 1, AC = 3 and ∠ BAC = (π)/(2) . If a circle of radius r… JEE Advanced 2022 Let a, b and c be the length of sides of a triangle ABC such that (a + b)/(7) = (b +… JEE Main 2022 Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q… JEE Advanced 2021 In a triangle ABC , let AB = 23 , BC = 3 and CA = 4 . Then the value of (cotA +… JEE Advanced 2021 Let (sinA)/(sinB) = ( ( A - C ))/( ( C - B )), where A, B, C are angles of a triangle ABC… JEE Main 2021 Let in a right angled triangle, the smallest angle be θ . If a triangle formed by taking… JEE Main 2021 If in a triangle ABC, AB = 5 units, ∠ B = ^ - 1 ((3)/(5)) and radius of circumcircle of ∆… JEE Main 2021 In Δ ABC, the lengths of sides AC and AB are 12cm and 5cm, respectively. If the area of ∆… JEE Main 2021 Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides… JEE Advanced 2020 Suppose that the side lengths of a triangle are three consecutive integers and one of the… NTA Abhyas JEE Main 2020 The inradius of the triangle having sides 26, 28, 30 units is NTA Abhyas JEE Main 2020 The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and… NTA Abhyas JEE Main 2020 Full Properties of Triangles list Properties of Triangles JEE Maths PYQs JEE Mathematics PYQs All JEE Advanced PYQs