draw a pair of tangents to a circle of radius 4cm which are inclined to each other at an angle of 45 degree.

Following the given steps in order to construct the tangents.

Step 1 : Draw a circle of radius 4 cm and centre O.

Step 2 : Take a point A on the circle. Join OA.

Step 3 : Draw a perpendicular to OA at A.

Step 4 : Draw a radius OB, making an angle of 135° (180° – 45°) with OA.

Step 5 : Draw a perpendicular to OB at point B. Let these perpendiculars intersect at P.

Here, PA and PB are the required tangents inclined at angle of 45°.