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Chord Theorem 2

The figure sh...

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

2.83 cm

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4cm

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2cm

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8cm

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Solution

The correct option is A 2.83 cm
$∠ P R Q h a s b e e n s u b t e n d e d b y t h e d i a m e t e r P Q t o t h e c i r c u m f e r e n c e a t R . ∴ ∠ P R Q i s a n a n g l e i n t h e s e m i c i r c l e . ∴ ∠ P R Q = 90^{o} s i n c e t h e a n g l e i n a s e m i c i r c l e = 90^{o} . S o Δ P Q R i s r i g h t a n g l e d w i t h P Q a s h y p o t e n u s e . A p p l y i n g P y t h a g o r a s t h e o r e m, w e h a v e, P Q = \sqrt{{P R}^{2} + {Q R}^{2}} = \sqrt{4^{2} + 4^{2}} c m = \sqrt{32} c m . ∴ t h e r a d i u s O P = O Q = \frac{1}{2} d i a m e t e r P Q = \frac{\sqrt{32}}{2} c m = 2.83 c m . A n s - O p t i o n A .$

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