Points A and B are at opposite ends of a circular pond...

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Points A and B are at oppositive ends of a circular pond with diameter d. A bridge connects point A with point C, and another bridge connects point C with point B. The two bridges are of equal lenght. What is the ratio of the distance from A to B when traveling along the two bridges to the distance when traveling along the edge of the pond?

$$A.\ \ \frac{2\cdot\sqrt{2}}{\pi}$$
$$B.\ \ \frac{d\cdot\sqrt{2}}{\pi}$$
$$C.\ \ \frac{2}{\pi}$$
$$D.\ \ \frac{\sqrt{2}}{2\cdot\pi}$$
$$E.\ \ \frac{2\cdot\sqrt{2}}{d\cdot\pi}$$

The OA is A.

Experts, I need your help with this PS question. I don't know how can I solve this question. I think that I can get two right triangles with the points ACO and BCO but I don't know what can I do with it later. Thanks in advance!

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by GMATWisdom » Sun Dec 17, 2017 2:19 pm
AAPL wrote:Image

Points A and B are at oppositive ends of a circular pond with diameter d. A bridge connects point A with point C, and another bridge connects point C with point B. The two bridges are of equal lenght. What is the ratio of the distance from A to B when traveling along the two bridges to the distance when traveling along the edge of the pond?

$$A.\ \ \frac{2\cdot\sqrt{2}}{\pi}$$
$$B.\ \ \frac{d\cdot\sqrt{2}}{\pi}$$
$$C.\ \ \frac{2}{\pi}$$
$$D.\ \ \frac{\sqrt{2}}{2\cdot\pi}$$
$$E.\ \ \frac{2\cdot\sqrt{2}}{d\cdot\pi}$$

The OA is A.

Experts, I need your help with this PS question. I don't know how can I solve this question. I think that I can get two right triangles with the points ACO and BCO but I don't know what can I do with it later. Thanks in advance!
If r is the radius of the circle AO=OB each would be =√(2 ) r
Therefore AO+OB = 2√(2 ) r
Distance A to B along the semicircle A=Ï€r
Hence ratio =2√(2 ) r/ πr=2√(2 )/r
Hence option A