Question

Construct a tangent from a point to a circle using just a compass and a straightedge.

Answer 1

Given: Circle with center $O$.
Construct: a tangent to circle at a point on the circle.
Steps:
1. A point is already given on the circle, draw a line and extend the radius past the circle.
2. Take a compass and measure three-fourth of the radius and draw a arc.
3. Construct a perpendicular line to the arc.
4. From the perpendicular line measure the length of line from radius and cut the circle on both the sides.
5. Join the point $PA$ and $PB$.
6. $PA$ and $PB$ are the two tangents to the given circle.