To construct a tangent from given conditions
1. Let us draw a circle of radius 5 cm and with the centre as O.
2. Considering a point Q on the circumference of the circle and join OQ.
3. Draw a perpendicular to QP at point Q.
4. Draw a radius OR, making an angle of 120° i.e(180°−60°) with OQ.
5. Draw a perpendicular to RP at point R.
6. Now both the perpendiculars intersect at point P.
7. Therefore, PQ and PR are the required tangents at an angle of 60°.
We have to prove that ∠QPR = 60°
∠OQP = 90°
∠ORP = 90°
And ∠QOR = 120°
We know that the sum of all interior angles of a quadrilateral = 360°
∠OQP+∠QOR + ∠ORP +∠QPR = 360o
90°+120°+90°+∠QPR = 360°
Therefore, ∠QPR = 60°