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In the diagram, P and Q are the centres of two circles with radii 9 cm and 4 cm respectively. MN is a common tangent to the circles. Calculate(a) the length of MN,(b) the value of x,(c) the perimeter of the shaded region.(Assume = 3.142)

PQMNSolution:Hx(a)PQ == 13 cmPT == 5 cmIn PQT,TQ2 = PQ2 PT2= 132 52 MN = 12 cmTQ = 12 cm9 + 49 4

PQMNSolution:Hx= 2.4x = 67.4T

PQMNSolution:Hx(c)Length of arc HM =HQN == 112.6TLength of arc HN= = 10.59 cm= 7.86 cmPerimeter of the shaded region =180 67.410.59 + 7.86 + 12 = 30.45 cm