Question

Draw ∆PQR such that PQ = 6.8 cm, vertical angle is 50° and the bisector of the vertical angle meets the base at D where PD = 5.2 cm

Answer 1

Steps of construction:

1. Draw a line segment PQ = 6.8 cm.

2. At P draw PE such that ∠QPE = 50°.

3. At P draw PF such that ∠EPF = 90°.

4. Draw the perpendicular bisector to PQ which intersects PF at O and PQ at G.

5. With O as centre and OP as radius draw a circle.

6. From P mark an arc of 5.2 cm on PQ at D.

7. The perpendicular bisector intersects the circle at I. Join ID.

8. ID produced meets the circle at A. Now Joint PR and QR. This ∆PQR is the required triangle.