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