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# Circles

In a triangle PQR, PQ= 12 cm, QR=10 cm and PR= 8 cm, a circle is inscribed touching PQ in L,QR in M and PR in N .

FIND ::::: PL , QM and RN

Note by Hariman Malhotra
3 years ago

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if we take PL as x,QM as y and RN as z

then we can see that x+y=12 x+z=10 y+z=8

on solving we get x=5 y=7 z=3 · 3 years ago

+1. The key to deriving the equations stems from knowing/proving the lengths of the tangents from the same point are equal. · 3 years ago

I also did same! · 3 years ago

thanks bro · 3 years ago

just saying about the question.......isnt it 10 th standard cbse maths book exercise question of chapter circles? · 3 years ago

You can generalize with side lengths a, b, c as

x + y = a

y + z = b

z + x = c

Adding, x + y + z = (a + b + c)/2 = s

So required lengths are $$\boxed {(s - a), (s - b), (s - c)}$$ · 3 years ago