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

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

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Construction Procedure:

The construction to draw a pair of tangents to the given circle is as follows.

1. Draw a circle with radius = 6 cm with centre O.

2. Locate a point P, which is 10 cm away from O.

3. Join the points O and P through line

4. Draw the perpendicular bisector of the line OP.

5. Let M be the mid-point of the line PO.

6. Take M as centre and measure the length of MO

7. The length MO is taken as radius and draw a circle.

8. The circle drawn with the radius of MO, intersect the previous circle at point Q and R.

9. Join PQ and PR.

10. Therefore, PQ and PR are the required tangents

To prove this, join OQ and OR represented in dotted lines.

From the construction,

∠PQO is an angle in the semi-circle.

We know that angle in a semi-circle is a right angle, so it becomes,

∴ ∠PQO = 90°

Such that

⇒ OQ ⊥ PQ

Since OQ is the radius of the circle with radius 6 cm, PQ must be a tangent of the circle. Similarly, we can prove that PR is a tangent of the circle.

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