Question

Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60°. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

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Answer 1

this is your answer............

Answer 2

Given:-

Radius of circle = r = 4cm

The angle formed by two tangent = 60°

To Find:-

Distance between center of circle and the point intersected by tangent i.e outside the circle.

• "Refer Attachment for rough diagram and construction."

Solution:-

Here a pair of tangent determines the tangent to a circle from a point outside the circle.

By tangent theorem

∠OAC = ∠OBC = 90°

also, △CAO = △CBO by AAS test of congruence

•°• ∠ACO = ∠BCO = 30°

In △CAO,

sin 30° = r/h

1/2 = 4/h

4 × 2 = h × 1 = 8 = h

•°• h = 8

Answer:-

Distance between center of circle and the point intersected by tangent i.e outside the circle = h = 8 cm