New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Properties of Triangle question

2023 · Shift 2 · Q31

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Properties of Triangle
2023 · Shift 2 · Q31

Properties of Triangle question

2023 · Shift 2 · Q31

JEE AdvancedMathematicsProperties of TriangleNumerical+3 / −1

Consider an obtuse angled triangle

A B C

in which the difference between the largest and the smallest angle is

\frac{\pi}{2}

and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.

\text { Let } a \text { be the area of the triangle } A B C \text {. Then the value of }(64 a)^2 \text { is }

:

Numerical answer

More from Properties of Triangle

In a triangle ABC, let AB = $23$ , BC = 3 and CA = 4. Then the value of $\frac{c o t A + c o t C}{c o t B}$ is .2021 · Numerical
Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE?2021 · Multiple correct
Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides of a triangle opposite to its angles X, Y, and Z, respectively. If $tan \frac{X}{2} + tan \frac{Z}{2} = \frac{2 y}{x + y + z}$ , then which of…2020 · Multiple correct
In a triangle PQR, let a = QR, b = RP, and c = PQ. If |a| = 3, |b| = 4 and $\frac{a . ( c - b )}{c . ( a - b )} = \frac{∣ a ∣}{∣ a ∣ + ∣ b ∣}$ , then the value of |a $\times$ b|2 is ......2020 · Numerical
In a non-right-angled triangle $Δ$ PQR, let p, q, r denote the lengths of the sides opposite to the angles At P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and…2019 · Multiple correct
In a triangle $Δ X Y Z$ , let $x, y, z$ be the lengths of sides opposite to the angles $X, Y, Z$ respectively, and $2 s = x + y + z$ . If $\frac{s - x}{4} = \frac{s - y}{3} = \frac{s - z}{2}$ and area of incircle of the triangle $X Y Z$ …2016 · Multiple correct
Match the following : Includes table2015 · MCQ
In a triangle the sum of two sides is $x$ and the product of the same sides is $y$ . If $x^{2} - c^{2} = y$ , where $c$ is the third side of the triangle, then the ratio of the in radius to the circum-radius of the triangle is2014 · MCQ