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Question

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then ar(RAS) is


Solution

In quadrant PLRM, rectangle PQRS is inscribed.
Radius of the circle  = 13 cm

A is any point on PQ.
AR and AS are joined, PS = 5 cm
In right PRS, PR2=PS2+SR2(13)2=(5)2+SR2169=25+SR2SR2=16925=144=(12)2SR=12cmArea of rectangle PQRS=PS×SR=5×12=60cm2
  Rectangle PQRS and RAS are on the same base SR and between the same parallels
Area RAS=12 Area of rectangle PQRS
 =12×60=30cm2

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