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Question

# Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

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Solution

## Steps of Construction: Step I: With O as a centre and radius equal to 4 cm, a circle is drawn. Step II: With O as a centre and radius equal to 6 cm, a concentric circle is drawn. Step III: P be any point on the circle of radius 6 cm and OP is joined. Step IV: Perpendicular bisector of OP is drawn which cuts it at M. Step V: With M as a centre and OM as a radius, a circle is drawn which intersect the circle of radius 4 cm at Q and R. Step VI: PQ and PR are joined. Thus, PQ and PR are the two tangents. Measurement: OQ = 4 cm (Radius of the smaller circle) PO = 6 cm ( Radius of the larger circle) ∠PQO=90∘ (Angle in the semi circle) Applying Pythagoras theorem in ΔPQO, PQ2+QO2=PO2 ⇒PQ2+42=62 ⇒PQ2+16=36 ⇒PQ2=36−16 ⇒PQ2=20 ⇒PQ=2√5cm Justification: ∠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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