(Q7). How can you draw the tangent to a circle at a given point when the center of the circle is not known?

Hint: Draw equal angles ∠QPX and ∠PRQ. Explain the construction.

PXYQR

Steps of construction

1. Take a point and draw a chord through P.

2. Construct ∠ and measure it.

3. Construct ∠ at P equal to ∠PRQ

4. Extend on other side. is the required tangent at P.

Note: Angle between a tangent a chord is equal to angle in the alternative segment