AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C, \frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}=\)
- A \(\frac{a^2+b^2+c^2}{\Delta^2}\)
- B \(\frac{a+b+c}{\Delta^2}\)
- C \(\frac{s^2}{\Delta^2}\)
- D \(\frac{4 s^2}{\Delta^2}\)
Answer & Solution
Correct Answer
(A) \(\frac{a^2+b^2+c^2}{\Delta^2}\)
Step-by-step Solution
Detailed explanation
\(\because\)\(r_1=\frac{\Delta}{s-a}\) \(\therefore\) \(\frac{1}{r_1}=\frac{s-a}{\Delta}\) Similarly, \(\frac{1}{r_2}=\frac{s-b}{\Delta} \frac{1}{r_3}=\frac{s-c}{\Delta}\) and \(\frac{1}{r}=\frac{s}{\Delta}\) Now, \(\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}\)…
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
- If the general solution set of \(\sin x+3 \sin 3 x+\sin 5 x=0\) is S , then \(\{\sin \alpha / \alpha \in S\}=\)AP EAMCET 2024 Medium
- In a \(\triangle \mathrm{ABC}\), if \(\mathrm{a}=13, \mathrm{~b}=14\) and \(\mathrm{c}=15\), then \(\sin\)AP EAMCET 2022 Easy
- If a circle with radius 2.5 units passes through the points \((2,3)\) and \((5,7)\), then its centre isAP EAMCET 2017 Medium
- Let \(\mathrm{A}\) and \(\mathrm{B}\) be two independent events of a random experiment. If the probability that both A and B occur is \(\frac{1}{6}\) and the probability that neither of them occur is \(\frac{1}{3}\), then the probability of occurrence of \(\mathrm{A}\) isAP EAMCET 2023 Hard
- If \(1, \omega, \omega^2\) are the cube roots of unity, then \((2-\omega)^2\left(2-\omega^2\right)^2\left(2-\omega^{10}\right)^2\left(2-\omega^{11}\right)^2=\)AP EAMCET 2022 Easy
- The distance of the point \((6,4 \sqrt{3})\) from the focus of \(y^2=8 x\) isAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- If \(\sin (x+3 \alpha)+3 \sin (x-\alpha)=0\), thenAP EAMCET 2017 Easy
- If \(x=a t^2\) and \(y=2 a t\), then \(\frac{d^2 y}{d x^2}\) at \(t=\frac{1}{2}\) isAP EAMCET 2015 Hard
- A box contains 4 defective and 6 good machines. Two machines are selected at random without replacement. Find the probability that both the machines are good.AP EAMCET 2020 Easy
- A magnetic field is applied on an electron moving with a velocity of \(10^7 \mathrm{~ms}^{-1}\) at an angle of \(30^{\circ}\). Then the time period of revolution of the electron in a circular path of radius \(2 \mathrm{~m}\) is ____AP EAMCET 2017 Easy
- If \(\int e^x(1+x) \cdot \sec ^2\left(x e^x\right) d x\) \(=f(x)+\) constant, then \(f(x)\) is equal toAP EAMCET 2008 Medium
- The work done to increase the volume of 2 moles of an ideal gas from V to 2 V at a constant temperature T is W. The work to be done to increase the volume of 2 moles of the same gas from 2 V to 4 V at the same constant temperature T isAP EAMCET 2025 Medium