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Question

The figure shows a circle with center O and diameter PQ. Point R lies on the circumference of the circle such that PR=QR and PR= 4 cm.The radius of the given circle (correct to two decimal places) is
182622_5b4ec597ff5e438888d61049b7113283.png

A
2.83 cm
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B
4cm
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C
2cm
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D
8cm
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Solution

The correct option is A 2.83 cm
PRQhasbeensubtendedbythediameterPQtothecircumferenceatR.PRQisanangleinthesemicircle.PRQ=90osincetheangleinasemicircle=90o.SoΔPQRisrightangledwithPQashypotenuse.ApplyingPythagorastheorem,wehave,PQ=PR2+QR2=42+42cm=32cm.theradiusOP=OQ=12diameterPQ=322cm=2.83cm.AnsOptionA.
238700_182622_ans_5d50ba977ed14259a57feab7e0934db2.png

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