Question

Take point P and Q and draw a circle passing through them. Draw a tangent AB to the circle without using the center of the circle.

Answer 1

Analysis:

Center of the circle passing through P and Q must be equidistant from points P and Q.

∴ It must lie of perpendicular bisector of seg PQ.

Steps of construction:

1. Take any two point P, Q and join them.
2. Draw a perpendicular bisector of PQ.
3. Take any point O on the perpendicular bisector and draw a circle with center O and radius OP.
4. Take any point A on the major arc of the circle and draw ∆PQA.
5. By taking P as center and any convenient distance on compass draw an arc intersecting the arms of ∠QPA in points T and R.
6. With A as center and the same distance in the compass, draw an arc intersecting the chord QA at point S.
7. Taking radius equal to TR and S as center, draw an arc intersecting the previously drawn arc. Name the point of intersection as B.
8. Draw line AB. Line AB is the required tangent to the circle.