In fig , a circle isinscribed in a triangle PQR with PQ = 10 cm , QR = 8 cm and PR = 12 cm .Find the length of the QM , RN and PL.

Explanation

We know that the lengths of the tangents drawn from an external point to a circle are equal.
Let `PL=PN=x`, `QL=OM=y`, `RM=RN=z`.
Now, `PL+QL=PQimpliesx+y=10`,……..`(i)`
`QM+RM=QRimpliesy+z=8`, ……….`(ii)`
`RN+PN=PRimpliesz+x=12`………`(iii)`
Subtracting `(ii)` from `(iii)`, we get `x-y=4` .....`(iv)`
Solving `(i)` and `(iv)`, we get `x=7`, `y=3`.
Substituting `y=3` in `(ii)`, we get `z=5`.
`:.QM=y=3cm`, `RN=z=5cm`, `PL=x=7cm`