Draw a circle with the help of a bangle. Take any point P outside the circle. Construct the pair of tangents from the point P to the circle. HINT See Example 6.

Question

Philoid · Accepted Answer

Steps of Construction:

1. Draw a circle with the help of a bangle. (implies center and radius of the circle is unknown)

2. Mark a point P outside the circle.

3. Draw a secant to this circle , PAB that intersect the circle at A and B.

4. Extend AP to C, such that PA = PC.

5. Draw perpendicular bisector of CB, which intersects CB at O.

6. With O as center, draw a semicircle passing through C and B.

7. From P, make an angle of 90° such that it cuts the semicircle at Q.

8. With P as center and PQ as the radius of the circle. Draw a circle that cuts the previous circle at K and L.

9. Join PK and PL. Then PK and PL are the required tangents.