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.
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.