Steps of construction:
(1) Draw a circle with center O and radius
(2) Draw a diameter A in the circle.
(3) At point A of OA, draw a ray OC making an angle of 45° to meet the circle.
(4) Draw line perpendicular to OB at B also draw a perpendicular line at C of OC, which intersects each other at P.
PB and PC are the required tangents that make an angle of 45° between them,
Proof : O is the center of circle and PB and PC are the tangents.
The angle between them ∠BPC = 45°.
∴ ∠BOC = 180° – 45° = 135°
∴ ∠AOC = 180° – ∠BOC (By pair of linear equation)
= 180° – 135° = 45°
