Let the radius of the circle is 5 cm

Steps of Construction:

1. Draw a circle of radius 5 cm with centre as O.

2. Take a point A on the circumference of the circle and join OA.

3. Draw a perpendicular to OA at A.

4. Draw a radius OB making an angle of 90 degree (180 - 90) with OA

5. Draw a perpendicular to OB at point B. Let the perpendiculars intersect at point P.

Now, PA and PB are the required tangents at an angle of 90 degree.