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Properties of Triangle

15 questions · Mathematics · JEE Advanced

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JEE Advanced
Mathematics
Properties of Triangle

Properties of Triangle

15 questions · Mathematics · JEE Advanced

Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{π}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of…2023 · Shift 2 · Q31 · Numerical
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 · Shift 1 · Q37 · 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 · Shift 2 · Q21 · 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 · Shift 1 · Q28 · 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 · Shift 1 · Q34 · 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 · Shift 1 · Q25 · 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 · Shift 1 · Q25 · Multiple correct
Match the following : Includes table2015 · Shift 1 · Q36 · 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 · Shift 2 · Q35 · MCQ
In a triangle $P QR$ , $P$ is the largest angle and $cos P = \frac{1}{3}$ . Further the incircle of the triangle touches the sides $P Q$ , $QR$ and $R P$ at $M$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive…2013 · Shift 2 · Q30 · Multiple correct
Let $P QR$ be a triangle of area $Δ$ with $a = 2$ , $b = \frac{7}{2}$ and $c = \frac{5}{2}$ ; 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 $\frac{2 s i n P - s i n 2 P}{2 s i n P + s i n 2 P}$ …2012 · Shift 2 · Q31 · MCQ
If the angles $C$ and $C$ of a triangle are in an arithmetic progression and if $c$ and $c$ denote the lengths of the sides opposite to $C$ and $C$ respectively, then the value of the expression $\frac{a}{c} sin 2 C + \frac{c}{a} sin 2 A$ …2010 · Shift 1 · Q39 · MCQ
Let $A B C$ be a triangle such that $∠ A C B = \frac{π}{6}$ and let $c$ and $c$ denote the lengths of the sides opposite to $A$ , $B$ and $C$ respectively. The value(s) of $x$ for which $a = x^{2} + x + 1, b = x^{2} - 1$ …2010 · Shift 1 · Q50 · MCQ
Consider a triangle $A B C$ and let $c$ and $c$ denote the lengths of the sides opposit to vertices $C$ and $C$ respectively. Suppose $a = 6, b = 10$ and the area of the triangle is $153$ , if $∠ A C B$ is obtuse and if $r$ …2010 · Shift 2 · Q30 · Numerical
Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2 $2$ and angle B = 30 $^{\circ}$ . The absolute value of the difference between the areas of these triangles is .2009 · Shift 2 · Q37 · Numerical