Question

Construct a $\Delta$ PQR such that PQ = $6$ cm, $\angle$QRP = ${45}^0$ and angle PQR = ${60}^0$ . Locate its incentre and draw its incircle.

Answer 1

Steps of Construction

1. Construct a line segment $PQ=6$ cm.

2. At the point P construct rays which make an angle of 450 and at point Q which makes an angle ${60}^{\circ }$ which intersects each other at point R.

3. Construct the bisectors of $\angle P$ and $\angle Q$ which intersect each other at point I.

4. From the point I construct IL which is perpendicular to PQ.

5. Taking I as Centre and IL as radius construct a circle which touches the sides of $\Delta$PQR internally.

This is the required incircle where the point I is incentre.