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

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## Comments

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TopNewestif 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

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

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I also did same!

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thanks bro

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

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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 \( \boxed {(s - a), (s - b), (s - c)} \)

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