Question

Draw a circle of radius 2.7 cm and draw a chord PQ of length 4.5 cm. Draw tangents at points P and Q without using centre.

Answer 1

Rough Figure:

Steps of construction:

1. Draw a circle of radius 2.7 cm.
2. Draw a chord PQ of length 4.5 cm.
3. Take a point A on the major arc, other than P and Q.
4. Join PA and QA.
5. Using P and Q as vertices and chord PQ as one side, draw ∠MPQ and ∠MQP equal to ∠PAQ.
6. Lines containing the rays PM and QM are the tangents to the circle at P and Q respectively.