Question

Jamal wants to construct a tangent line to circle O that passes through point M. He started by drawing a segment from point O to point M. Next he constructed the midpoint of segment OM. What is the next step in his construction.

Answer 1

To draw the tangent line through the point M , which lies in the external of circle, having center O

1.Join OM.

2. Find the mid point of OM using Perpendicular bisector method to find the Bisector of Segment OM.To draw the perpendicular bisector, taking more than half of segment OM , mark arc on both sides of segment OM from point O and M.The two arcs intersect at two points S and T.Join S and T.Let it cuts the segment at point N.

3. Now, if the mid point of Segment OM is N, the taking N as center and ON or MN as Radius, mark arcs on circle at two points P and Q.

4. Join PM and QM.

These are the two tangents from external point M .

Answer 2

Draw circle O then draw point M, and connect point M to center O. Then find the midpoint of the segment OM. After drawing a midpoint of segment OM, draw a line from point M which will pass through any point of the circle O. This line will be the tangent of the circle that passes through point M.