AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), if \((a-b)(s-c)=(b-c)(s-a)\), then \(r_1, r_2, r_3\) are in
- A Arithmetic progression
- B Geometric progression
- C Harmonic progression
- D Arithmetico - geometric progression
Answer & Solution
Correct Answer
(A) Arithmetic progression
Step-by-step Solution
Detailed explanation
Given: \((a-b)(s-c)=(b-c)(s-a)\) \(\begin{aligned} & \Rightarrow[(s-a)-(s-b)](s-c)=[(s-b)-(s-c)](s-a) \\ & \Rightarrow(s-a)(s-c)-(s-b)(s-c) \\ & =(s-b)(s-a)-(s-c)(s-a)\end{aligned}\) Dividing by \((s-a)(s-b)(s-c)\) on both sides, we get…
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 equation of the polar of the point \((\alpha,-1)\) with respect to the circle \(x^2+y^2-4 x-6 y-12=0\) is \(y=\beta\), then \(4(\alpha+\beta)=\)AP EAMCET 2025 Medium
- \(\int e^{4 x^2+8 x-4}(x+1) \cos \left(3 x^2+6 x-4\right) d x=\)AP EAMCET 2024 Medium
- For a circle of diameter \(R\), touching \(x^2+y^2-4 y=0\) and passing through \((4,5)\), which of the following is correct?AP EAMCET 2022 Easy
- The equations of the tangent to the circle \(5 x^2+5 y^2=1\) parallel to the line \(3 x+4 y=1\) areAP EAMCET 2021 Medium
- The equation of a circle with center at \((-2,3)\) and circumference of \(4 \pi\) units isAP EAMCET 2021 Easy
- \(\int_{-1 / 24}^{1 / 24} \sec x \log \left(\frac{1-x}{1+x}\right) d x=\)AP EAMCET 2024 Hard
More PYQs from AP EAMCET
- Which of the following is incorrectly matched?AP EAMCET 2024 Medium
- A truck moving with a constant velocity \(12 \mathrm{~ms}^{-1}\) crosscs a car moving from rest with uniform acceleration \(2 \mathrm{~ms}^{-2}\). The distance the car has to travel from the starting point to cross the truck again isAP EAMCET 2023 Easy
- If , then the ratioAP EAMCET 2021 Hard
- \(\mathrm{A}=(-2,0)\) and \(\mathrm{P}\) is a point on the parabola \(y^2=8 x\). If \(\mathrm{Q}\) bisects \(\overline{\mathrm{AP}}\) and the locus of \(\mathrm{Q}\) is a parabola, then its focus isAP EAMCET 2017 Easy
- Two charges \(+q\) and \(-q\) are kept apart. Then at any point on the right bisector of line joining the two chargesAP EAMCET 2008 Easy
- If the position vectors of the vertices of a triangle are \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \quad \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\), then the triangle isAP EAMCET 2002 Medium