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For a lezim kavayat the girls of standard IX are arranged in two circular concentric rings as shown in the figure if PA = 15 m, PR = 25 m, QR = 10 m, then the measures of RS, PQ, QT are

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20,

15 \sqrt{5}

, 30

40,

5 \sqrt{5}

, 60

40,

15 \sqrt{5}

, 60

None of these

answer is C.

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Detailed Solution

Consider ∠PAR and ∠PAQ from the triangles PAQ and PAR.
Both are perpendicularly drawn from the center of the circle to the chord RS.

{PR}^{2} = {PA}^{2} + {AR}^{2}

\Rightarrow 25^{2} = 15^{2} + {AR}^{2}

\Rightarrow {AR}^{2} = 625 - 225 = 400 = 20^{2}

\Rightarrow AR = 20

RS = 2AR = 40
QA = QR + AR = 10 + 20 = 30
QT = 2QA = 60
In triangle PQA,

{PQ}^{2} = {PA}^{2} + {QA}^{2}

\Rightarrow {PQ}^{2} = 15^{2} + 30^{2}

\Rightarrow {PQ}^{2} = 225 + 900 = 1125 = {(15 \sqrt{5})}^{2}

\Rightarrow PQ = 15 \sqrt{5}

So, Option 3 is correct.

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