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kryton1212

  • 2 years ago

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.

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  1. kryton1212
    • 2 years ago
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    |dw:1355634883499:dw|

  2. mathstudent55
    • 2 years ago
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    |dw:1355637343376:dw|

  3. mathstudent55
    • 2 years ago
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    |dw:1355637938345:dw|

  4. kryton1212
    • 2 years ago
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    I have think about it but I cannot do furthermore...

  5. mathstudent55
    • 2 years ago
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    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

  6. kryton1212
    • 2 years ago
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    wait a moment....

  7. kryton1212
    • 2 years ago
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    got it. then I know part b :) thank you

  8. mathstudent55
    • 2 years ago
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    (AP)^2 + (OP)^2 = r^2 64 + (1.5)^2 = r^2 r^2 = 66.25 r^2 = 265/4 r = sqrt(265)/2

  9. kryton1212
    • 2 years ago
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    thank you very much

  10. mathstudent55
    • 2 years ago
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    You're very welcome.

  11. gerryliyana
    • 2 years ago
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    @kryton1212

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