In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT=65o, find the value of x, y and z.
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Solution
In △OSP, ∠OSR=90o [Radius is perpendicular to tangent] In △TSR x+90o+65o=180o ∴x=25o ∠SOQ=2∠STR [Angle at centre =2× Angle at circumference] y=2×25=50o In △OSP, 50o+90o+z=180o ∴z=40o