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Question
In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°,
find the value of x, y and z.
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Solution
In the given figure, TS ⊥ SP,
m∠TSR = m∠OSP = 90°
In `triangle TSR, m angleTSR + m angleTSR + m angle RTS = 180^@`
`=> 90^@ + 65^@ + x = 180^@`
`=> x = 180^@ - 90^@ - 65^@`
`=> x= 25^@`
Now, y = 2x [Angle subtended at the centre is double that of the angle subtended by the arc at the same centre]
`=> y = 2 xx 25^@`
`:. y = 50^@`
In `triangle OSP ,m angleOSP + m angle SPO + m angle POS =180^@`
`=> 90^@ + z + 50^@ = 180^@`
`=> z = 180^@ - 140^@`
`:. z=40^@`
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