Question

.Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the

pair of tangents to the circle.​

Answer 1

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Answer 2

Step-by-step explanation:

Given:-

A circle of radius 6 cm. From a point 10 cm away from its centre

To find:-

Construct the pair of tangents to the circle.

Solution:-

Rough diagram:-

See the attachment

Construction:-

See the above attachment

Steps of Construction:-

• Draw a circle with the radius 6 cm of centre O.

• Take a point P 10 cm away from the centre of the circle and join O and P.

• Draw perpendicular bisectors XY of OP

• Mark intersecting point of XY to OP as M

• Draw a circle with the radius OM = MP .

• The new circle touches the first circle at A and B.

• Join P and A , P and B.

• PA and PB are the pair of tangents to the given circle and PA= PB = 8cm

• ∆AOP is congruent to ∆BOP,by Pythagoras theorem , OP^2=OA^2+AP^2

=> 10^2=6^2+AP^2

=> 100-36 = PA^2

=>PA^2=64

=> PA=√64

=> PA=8 cm

PA=PB = 8cm