## 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.

1. kryton1212

|dw:1355634883499:dw|

2. mathstudent55

|dw:1355637343376:dw|

3. mathstudent55

|dw:1355637938345:dw|

4. kryton1212

I have think about it but I cannot do furthermore...

5. 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

6. kryton1212

wait a moment....

7. kryton1212

got it. then I know part b :) thank you

8. 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

9. kryton1212

thank you very much

10. mathstudent55

You're very welcome.

11. gerryliyana

@kryton1212