Question

In the given figure, a circle inscribed in $\Delta PQR$ with PQ = 10 cm, QR = 8 cm. PR= 12 cm, find the length QM, RN and PL.

Answer 1

Here, $PL=PN,LQ=LM,RM=RN$ (Tangents from an exterior point to a circle are equal)

Let PL$=xcm$

Then , PN$=xcm$ (Because PL=PN) ........1

Now , PQ$=10cm$ Therefore,$LQ=(10-x$)cm

Then QM=$(10-x)cm$ (Because LQ=LM)

Now , QR=8cm Therefore MR$=8-(10-x)=(x-2)cm$

Then NR$=(x-2)cm$ (Because RM=RN)

Now,PR=12 cm Therefore,$PN=12-(x-2)cm$=$(14-x)cm$ ...............2

From eq 1 and 2 we have,$x=14-x$

$x=7cm$

Therefore ,$QM=10-7=3cm$

$RN=7-2=5cm$

$PL=7cm$