0

Guest

Courses New

in a triangle ABC a-b/b-c=s-a/s-c then exradii r1,r2,r3 are in a)AP b)GP c)HP

in a triangle ABC a-b/b-c=s-a/s-c then exradii r1,r2,r3 are in
a)AP
b)GP
c)HP

Grade:11

1 Answers

mycroft holmes
272 Points
6 years ago
You have \frac{s-a}{a-b} = \frac{s-c}{b-c}
 
Subtracting 1 from both sides you get \frac{s-b}{a-b} = \frac{s-b}{b-c} \Rightarrow a-b = b-c
 
Hence a,b,c are in AP, and so s-a, s-b, s-c are in AP and hence
 
\frac{s-a}{\Delta} , \frac{s-b}{\Delta} , \frac{s-c}{\Delta} are in AP
 
i.e. \frac{1}{r_1} , \frac{1}{r_2} ,\frac{1}{r_3} are in AP
 
and hence the ex-radii are in HP

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More