Question

Construct a $\Delta$PQR with QR = 8 cm, PQ = 7 cm, PR = 5 cm. Construct the incircle of the triangle and find the radius of the incircle.

Answer 1

1. Draw QR = 8 cm

2. With Q as a centre, draw an arc of radius 7 cm and with R as centre, draw an arc of radius 5 cm. Let these arcs intersect each other at point P.

3. Draw angle bisectors of $\angle$PQR and $\angle$PRQ, which intersect at point O.

4. Through point O, draw OA $\perp$ QR.

5. With O as centre and OA as radius, draw the required incircle which will touch all the three sides of the triangle.

6. Measure OA, the radius of the incircle.

7. Radius of incircle = 1.7 cm