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Question

In the given figure, PT touches a circle whose centre is O at R. Diameter SQ produced meets PT at P. If SPR=x and QRP=ycirc, then which of the following statements relate x and y?


A

x+2y=90

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B

x+y=90

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C

x+2y=45

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D

x=2y

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Solution

The correct option is A

x+2y=90


PT is a tangent to the circle (given)

QRP=QSR=y (angle in the alternate segment are equal)

QS is diameter of the circle (given)

QRS=90 (angle in the semi circle)

In PSR,x+y+90+y=180 (sum of angles of a triangle)

x+2y=90 Hence (A)


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