Ex 11.2, 7
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
In this question, we need to find center of circle first.
To find center,
1.We take any two non-parallel chords
2.And then finding the point of intersection of their perpendicular bisectors.
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.