Question

Draw a pair of tangents to a circle which are inclined to each other at an angle of ${80}^{\circ }$.

Answer 1

The tangents can be constructed in the following manner:
Step 1: Draw a circle of radius 5 cm and with centre as O
Step 2: Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A.
Step 3: Draw a radius OB, making an angle of $({180}^{\circ }-{80}^{\circ })$ with OA
Step 4: Draw a perpendicular to OB at point B. Let both the perpendiculars intersect at point P. PA and PB are the required tangents at an angle of ${80}^{\circ }$