anonymous
  • anonymous
In the figure, AB//CD and they are 4 cm apart. P and Q are the mid-points of AB and CD respectively. If AB=16 cm and CD=12 cm, find: (a) the length of OP (b) the radius of the circle.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
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mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
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anonymous
  • anonymous
I have think about it but I cannot do furthermore...
mathstudent55
  • mathstudent55
Right triangle AOP has legs AP and OP and hypotenuse OA Right triangle COQ has legs CQ and OQ and hypotenuse OC Because they're both radii, OA = OC = r For right triangle AOP, (OP)^2 + (AP)^2 = r^2 For right triangle COQ, (CQ)^2 + (OQ)^2 = r^2 By substitution, (OP)^2 + (AP)^2 = (CQ)^2 + (OQ)^2 Substitue values we know: (OP)^2 + 64 = 36 + (OP + 4)^2 (OP)^2 + 64 = 36 + (OP)^2 + 8(OP) + 16 Subtract (OP)^2 from both sides 64 = 36 + 8(OP) + 16 8(OP) = 12 OP = 1.5
anonymous
  • anonymous
wait a moment....
anonymous
  • anonymous
got it. then I know part b :) thank you
mathstudent55
  • mathstudent55
(AP)^2 + (OP)^2 = r^2 64 + (1.5)^2 = r^2 r^2 = 66.25 r^2 = 265/4 r = sqrt(265)/2
anonymous
  • anonymous
thank you very much
mathstudent55
  • mathstudent55
You're very welcome.
anonymous
  • anonymous
@kryton1212

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