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Question

In the given figure, PT is a tangent of a circle, with centre O, at point R. If diameter SQ is produced, it meets with PT at point P with SPR=x and QSR=y,then find the value of x+2y.


A

45

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B

60

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C

90

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D

150

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Solution

The correct option is C

90



In the given figure, OR=OS (Radii)
ORS=OSR=y(Angles opposite to equal sides are equal)

Also, ORP=90(Radius of a circle is perpendicular to the tangent at the point of contact.)

So, PRS=ORP+ORS=90+y

In ΔPRS,
SPR+PSR+PRS=180(Angle sum property of a triangle)
x+y+90+y=180x+2y=90


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