MathematicsFor 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

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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  1. A
    20, 155, 30
  2. B
    40, 55, 60
  3. C
    40, 155, 60
  4. D
    None of these 

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    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.
    PR2=PA2+AR2
    252=152+AR2
    AR2=625-225=400=202
    AR=20
    RS = 2AR = 40
    QA = QR + AR = 10 + 20 = 30
    QT = 2QA = 60
    In triangle PQA,
    PQ2=PA2+QA2
    PQ2=152+302
    PQ2=225+900=1125=1552
    PQ=155
    So, Option 3 is correct.
     
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