Question

The incircle of angle PQR is drawn . If PX =2.5 cm , Rz = 3.5 cm and perimeter of angle PQR = 18 cm , find the length of qy .

Answer 1

perimeter =PQ+QR+PR
18=PX+XQ+QY+YR+RZ+PZ
18=PX+QY+QY+RZ+RZ+PX( BECAUSE TANGENT DRAWN FROM SAME EXETERNAL POINTS ARE EQUAL)
9=PX+QY+RZ
9=2.5+QY+3.5
QY=3

Answer 2

Given:

PX=2.5cm, RZ=3.5cm.

Perimeter of ΔPQR=18cm.

To find:

QY

Step-by-step explanation:

Step 1 of 2

The tangents drawn from a point outside of circle to the circle are equidistant.

So, PX = PZ = 2.5cm

RZ = RY = 3.5cm

And QX = QY = x

Step 2 of 2

The perimeter of triangle = PR + RQ +PQ

$18=(2.5+3.5)+(x+3.5)+(x+2.5)\\\\18=12+2x\\\\18-12=2x\\\\6=2x\\\\x=3cm$

Therefore, QY = 3cm.