Question

Draw a circle of radius 4.2 cm. Draw arc PQ measuring 120°. Draw a tangent to the circle from point P and point Q.

Answer 1

Analysis:

Let O be the centre of the circle.

Here, ∠POQ = m(arc PQ)   ...[Definition of measure of minor arc]

∴ On drawing ∠POQ = 120°, we get an arc

PQ measuring 120°.

line `l` and line m are tangents to the circle.

line `l` ⊥ seg OP and line m ⊥ seg OQ   ...[Tangent theorem]

∴ To get tangents `l` and m, we draw perpendiculars to seg OP and seg OQ at points P and Q respectively.

Steps of construction:

1. Draw a circle of radius 4.2 cm with centre O.
2. Draw rays OP and OQ such that ∠POQ = 120°. (Points P and Q must be on the circle.)
3. Draw line `l` ⊥ ray OP at point P.
4. Draw line m ⊥ ray OQ at point Q.
   Line `l` and m are the required tangents.