TS EAMCET · Maths · Properties of Triangles
If \(A B C\) is an isosceles triangle with base \(B C\), then \(r r_1=\)
- A \(R^2 \cos ^2 A\)
- B \(\frac{a^2}{2}\)
- C \(\frac{r}{R}\)
- D \(R^2 \sin ^2 A\)
Answer & Solution
Correct Answer
(D) \(R^2 \sin ^2 A\)
Step-by-step Solution
Detailed explanation
\(r=\frac{\Delta}{s}, r_1=\frac{\Delta}{s-a}\) \(\begin{aligned} & r r_1=\frac{\Delta^2}{s(s-a)} \\ & =\frac{s(s-a)(s-b)(s-c)}{s(s-a)}\end{aligned}\) \(=(s-b)(s-c)=(s-b)^2 \quad(\because {~b}={c})\) \(=\frac{(2 s-2 b)^2}{4}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are need isTS EAMCET 2012 Easy
- \(A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]\) then \(A^3-4 A^2-6 A\) is equal to :TS EAMCET 2006 Medium
- \(\int_0^2 \frac{2 x-2}{2 x-x^2} d x\) is equal toTS EAMCET 2004 Easy
- Let \(A\) and \(B\) be not mutually exclusive events. If \(P(A)=\frac{4}{9}, P(A \cap \bar{B})=\frac{3}{7}\) then \(P\left(\frac{B}{A}\right)=\)TS EAMCET 2020 Easy
- If tangents are drawn from any point on the circle \(x^2+y^2=25\) to the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\), then the angle between the tangents isTS EAMCET 2014 Easy
- \(\int \frac{1}{16-7 \sin ^2 x} d x=\)TS EAMCET 2023 Medium
More PYQs from TS EAMCET
- Let the roots of the equation \(E_1 \equiv x^3+x^2+l x+n=0\) be \(x_i,(i=1,2,3)\) and the roots of \(E_2 \equiv x^3+a x^2+b x+c=0\) be \(\frac{x_i-1}{2}\). If the equation \(E_2=0\) is a equation of class one, then the roots of these two equations excluding the common roots areTS EAMCET 2020 Medium
- The wrong statement in the following isTS EAMCET 2020 Medium
- For the parabola the ends of the latus rectum are at and , thenTS EAMCET 2021 Medium
- If the energy gap of a semiconductor used for the fabrication of an LED is nearly 1.9 eV, then the color of the light emitted by the LED isTS EAMCET 2025 Easy
- The values of \(p\) and \(q\) so that the function \[ f(x)=\left\{\begin{array}{cl} (1+\mid \sin x)^{\frac{p}{\sin x}}, \frac{-\pi}{6} < x < 0 \ q & , x=0 \ e^{\frac{\sin 2 x}{\sin 3 x}} & , 0 < x < \frac{\pi}{6} \end{array}\right. \] is continuous at \(x=0\), areTS EAMCET 2016 Hard
- A rigid body of mass and radius rolls without slipping on an inclined plane of inclination under gravity. Match the type of body Column I with magnitude of the force of friction Column II.
Column I Column II A) For ring I) B) For solid sphere II) C) For solid cylinder III) D) For hallow cylinder IV) TS EAMCET 2021 Medium