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Question

# Question 1 Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

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Solution

## Steps of Construction: Step I: With O as a centre and radius equal to 6 cm, a circle is drawn. Step II: A point P at a distance of 10 cm from the centre O is taken. OP is joined. Step III: Perpendicular bisector of OP is drawn and it intersects OP at M. Step IV: With M as a centre and OM as a radius, a circle is drawn intersecting the previous circle at Q and R. Step V: PQ and PR are joined. Thus, PQ and PR are the tangents to the circle. On measuring the length, tangents are equal to 8 cm. PQ = PR = 8cm. Justification: OQ is joined. ∠PQO=90∘ (Angle in the semi-circle) ∴OQ⊥PQ Therefore, OQ is the radius of the circle then PQ has to be a tangent of the circle. Similarly, PR is a tangent of the circle.

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