Q.22. In the given diagram, PQ and RS are common tangents to the two circles with centres C and D the which of the following is true ?


(A) PQ = 13 cm
(B) PQ = 10 cm
(C) RS = 13 cm
(D) area of trapezium RSCD is 78 c m 2
 

Draw CLDS.We know that tangent to a circle is always  to its radius at the point of contact.Now, CLSR is a parallelogramNow, LS = CR   Opposite sides of parallelogram are equalNow, CL = RS  Opposite sides of parallelogram are equalNow, DL = DS - LS = 9 - 4 = 5 cmIn DLC,CD2 = CL2 + DL2                    Pythagoras theorem132 = CL2 + 52CL2 = 169 - 25 = 144CL = 12 cmNow, RS = CL = 12 cmLet d = D = 13cm; r1 = 9 cm' r2 = 4 cmNow, PQ = d2 + r1 - r22 = 132 + 52 = 12 cmArea of trapezium RSD = 12CR + DS×RS=124+9×12=78 cm2So, option D is correct.

  • 4
correct option may be c
  • -3
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