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Question

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.
577428_1a31c15765af495f9c642beb60248929.png

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Solution

In OSP, OSR=90o [Radius is perpendicular to tangent]
In TSR
x+90o+65o=180o
x=25o
SOQ=2STR
[Angle at centre =2× Angle at circumference]
y=2×25=50o
In OSP,
50o+90o+z=180o
z=40o

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