AP EAMCET · Maths · Properties of Triangles
In any \(\triangle A B C, r_1 r_2+r_2 r_3+r_3 r_1\) is equal to
- A \(\frac{\Delta^2}{r^2}\)
- B \(\frac{\Delta}{r}\)
- C \(\frac{2 \Delta}{r}\)
- D \(\Delta^2\)
Answer & Solution
Correct Answer
(A) \(\frac{\Delta^2}{r^2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { In } \triangle A B C, \\ & =\frac{\Delta}{s-a} \cdot \frac{\Delta}{s-b}+\frac{\Delta}{s-b} \cdot \frac{r_1 r_2+r_2 r_3+r_3 r_1}{s-c}+\frac{\Delta}{s-c} \cdot \frac{\Delta}{s-a} \\ & =\frac{\Delta^2}{(s-a)(s-b)(s-c)}[s-c+s-a+s-b]\end{aligned}\)…
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 plane \(7 x+11 y+13 z=3003\) meets the co-ordinate axes in \(A, B, C\), then the centroid of the \(\triangle A B C\) isAP EAMCET 2002 Easy
- If \(\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3\) are the vertices of an equilateral triangle and \(\mathrm{z}\) is its circum centre, thenAP EAMCET 2023 Easy
- Suppose \(A\) and \(B\) are the points at which the line \(x+y-\lambda=0\) meets the pair of straight lines \(x^2+y^2-2 x-4 y+2=0\). If \(\angle A O B=90^{\circ}\), then a value of \(\lambda\) isAP EAMCET 2022 Medium
- \(\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x=\)AP EAMCET 2023 Medium
- The ordinates of the points on the curve \(y=\tan ^{-1}\) \((\sin \sqrt{x}), 0 \leq x \leq 8 \pi^2\), at which the tangent is parallel to \(\mathrm{x}\)-axis areAP EAMCET 2023 Medium
- If \(f(x)= \begin{cases}\frac{\cos a x-\cos b x}{x^2}, & x \neq 0 \\ \frac{1}{2}\left(a^2-b^2\right) & , x=0\end{cases}\)
where \(a, b\) are real and district constants, thenAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- If \(\binom{\mathrm{p}}{\mathrm{q}}={ }^{\mathrm{p}} \mathrm{C}_{\mathrm{q}}\) and \(\sum_{\mathrm{i}=0}^{\mathrm{m}}\binom{10}{\mathrm{i}}\binom{20}{\mathrm{~m}-\mathrm{i}}\) is maximum, then \(\mathrm{m}=\)AP EAMCET 2025 Medium
- Let \(\pi\) be the plane passing through the point \((3,-3,1)\) and perpendicular to the line joining the points \((3,4,-1)\) and \((2,-1,5)\). If the equation of the plane containing the points \((3,4,-1),(-1,2,5)\) and perpendicular to the plane \(\pi\) is \(a x+y+c z-d=0\), then \(3(a+c)=\)AP EAMCET 2022 Hard
- If the function \(y=\sin x(1+\cos x)\) is defined in the interval \([-\pi, \pi]\), then \(y\) is strictly increasing in the intervalAP EAMCET 2025 Medium
- A \(1 \mathrm{~kg}\) ball moving with a speed of \(6 \mathrm{~ms}^{-1}\) collides headon with a \(0.5 \mathrm{~kg}\) ball moving in the opposite direction with a speed of \(9 \mathrm{~ms}^{-1}\). If the coefficient of restitution is \(\frac{1}{3}\), then the energy lost in the collision isAP EAMCET 2016 Hard
- A five digit number is formed by the digits with no digit being repeated. The probability that the number is divisible by , isAP EAMCET 2022 Easy
- In which of the following reactions, the product is not correct?AP EAMCET 2016 Medium