Question

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.

Answer 1

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

Answer 2

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

Answer 3

wait a moment....

Answer 4

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

Answer 5

(AP)^2 + (OP)^2 = r^2
64 + (1.5)^2 = r^2
r^2 = 66.25
r^2 = 265/4
r = sqrt(265)/2

Answer 6

thank you very much

Answer 7

You're very welcome.

Answer 8

@kryton1212