**Ex 11.2, 1**

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.

A pair of tangents to the given circle can be constructed as follows.

- Taking any point O of the given plane as centre, draw a circle of 6 cm radius. Locate a point P, 10 cm away from O. Join OP.
- Bisect OP. Let M be the mid-point of PO.
- Taking M as centre and MO as radius, draw a circle.
- Let it intersect the given circle at the points Q and R.
- Join PQ and PR.

Then, PQ and PR are the required two tangents.

After measuring, lengths of tangents PQ and PR are **8 cm each**.

**Justification:**

__We ____need to prove that PQ and PR are the tangents to the circle.__

Join OQ and OR.

∠PQO is an angle in the semi-circle

of the blue circle

And we know that angle in a

semi-circle is a right angle.

∴ ∠PQO = 90°

⇒ OQ ⊥ PQ

Since OQ is the radius of the circle,

PQ has to be a tangent of the circle.

Similarly, PR is a tangent of the circle.