What is b in the circle shown above? (1) bc = 5a (2) The length of PQ

GMATinsight Can you please elaborate explanation of 2nd statement ?

Hi vipulshahi!

Sorry for this "intrusion", but I will explain each statements alone, in detail, in the post below.

I hope you are able to clear your doubts. (Otherwise, I am sure GMATinsight will be most glad to help you!)

Regards,
Fabio.

Could you further clarify the explanation for statement two?

Hi, rZAhyYJtj !

Thank you for your interest in my solution.

01. By the similarity of the triangles mentioned (first line of statement (2)), we get the ratios´s equality in which only "b" (our FOCUS) is present!
02. Cross-multiplying and making the change-of-variables (k= b squared) we get a second-degree equation in the auxiliary k variable.
03. The "c/a" formula (Viète) gives us the product of the roots of a second-degree equation (when it has roots (*)).
(*) Obs.: it´s an examiner´s burden to guarantee that at least one b (therefore k) is viable... hence delta is nonnegative for sure, no need to check!
04. From the fact that the product of the two roots k1 and k2 is negative, only one of them is viable (the positive one), hence we know b^2 is this k.
05. From the fact that b is the square root of k or the opposite of the square root of k, we must take the first option (b>0). Therefore b viable is unique.

I hope you enjoy the arguments. If you believe you have the profile for a very high-level quant preparation, do not hesitate to do our test-drive!

Regards,
Fabio.

Hi, Can you please explain how the 3 triangles are similar triangles ?