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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.

1. 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.
2. Bisect OP. Let M be the mid-point of PO.
3. Taking M as centre and MO as radius, draw a circle.
4. Let it  intersect the given circle at the points Q and R.
5. 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.

1. Chapter 11 Class 10 Constructions
2. Concept wise
3. Constructing tangent from external point

Transcript

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.

Constructing tangent from external point