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Bunuel
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Jabjagotabhisavera
Alexey1989x
(1) following to properties of right triangles, if AC is diameter then angle ABC = 90 ===> side angles BAC=BCA=x are 45.
Since we don't know whether BC=CD we cannot define angle y..

Hi Alexey,

The question is not asking us to find out the value of y. Its asking for value of x only.


Looks like I missed the point :) Thanks for notice!
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Bunuel

AC is a diameter of the circle and B is a point on the circle. ACD is a straight line. What is the value of x?

(1) AB = BC
(2) x = 2y


Attachment:
2017-10-18_1037.png
I think the ănswer is C. We can deduce from the question that 3d^ + a^ = 180, 2a^+ d^ = 180 -> a^ = x = 72
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(1) A diameter subtends a right angle on the circle so given AB=BC, it is an isosceles triangle with x=45 degrees.

(2) We cannot deduce x with the given information.

A is the answer


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I went with answer A. AB=AC implies that it is an isosceles triangle with 45 degree angles at BCA and BAC.

St2 is insufficient, CD could be extremely far away and thus making the degree of BDC smaller. We'd also need to know the angle of ABD, which we don't have.
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