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.
Steps of construction
Draw a circle of radius 6 cm
Draw point P, 10 cm away from center
3. Join PO.
Make perpendicular bisector of PO
Let M be the midpoint of PO.
4. Taking M as centre and MO as radius,
draw a circle.
5. Let it intersect the given circle at points Q and R.
6. Join PQ and PR.
∴ PQ and PR are the required two tangents.
After measuring, lengths of tangents PQ and PR are 8 cm each.
4. Taking M as centre and MO as radius,
draw a circle.
5. Let it intersect the given circle at points Q and R.
6. Join PQ and PR.
∴ 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.
Now,
∠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

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.