Question

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°

Answer 1

Method 1:

• Draw a circle of radius = 5 cm.
• Draw X and Y axes through the center C of the circle.
• Let AOA' be the horizontal diameter and BOB' be the vertical diameter.
• Follow the procedure for trisecting the angle AOB. Let OC be the line that makes 30 deg and OD be the line that makes 60 deg with X axis.
• Follow the same procedure for trisecting the angle AOB' below X axis. Let OC' and OD' be lines that make 30 and 60 deg respectively.
• Draw perpendiculars to OD and OD' at D and D' respectively meeting X axis at one point P.
• PD and PD' are the tangents with an angle 60 deg between them.

Method 2:

• Draw the circle with center O and radius 5 cm.
• Find the point E 2.5 cm to the left of O on X axis (horizontal diameter). OE = 2.5 cm.
• Draw a perpendicular line to X axis at E. It meets the circle at D and D'.
• Draw perpendiculars to OD and OD' at D and D' meeting X axis at P exactly.
• PD and PD' are tangents.

Diagram is given in above previous Solution, hope this helps