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AC is a diameter of the circle and B is a point on the circle. ACD is

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AC is a diameter of the circle and B is a point on the circle. ACD is [#permalink]

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New post 17 Oct 2017, 23:39
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  55% (hard)

Question Stats:

71% (01:24) correct 29% (01:12) wrong based on 55 sessions

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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
2017-10-18_1037.png [ 14.65 KiB | Viewed 1553 times ]

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AC is a diameter of the circle and B is a point on the circle. ACD is [#permalink]

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New post Updated on: 19 Oct 2017, 00:58
(1) following to properties of right triangles, if AC is diameter then angle ABC = 90 ===> side angles BAC=BCA=x are 45.

(2) since we don't know if AB=BC we cannot define the value of angle x


Answer A.

Originally posted by Alexey1989x on 17 Oct 2017, 23:54.
Last edited by Alexey1989x on 19 Oct 2017, 00:58, edited 1 time in total.
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Re: AC is a diameter of the circle and B is a point on the circle. ACD is [#permalink]

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New post 19 Oct 2017, 00:45
1
Alexey1989x wrote:
(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.
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Re: AC is a diameter of the circle and B is a point on the circle. ACD is [#permalink]

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New post 19 Oct 2017, 00:58
Jabjagotabhisavera wrote:
Alexey1989x wrote:
(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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Re: AC is a diameter of the circle and B is a point on the circle. ACD is [#permalink]

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New post 19 Oct 2017, 01:10
Bunuel wrote:
Image
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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Re: AC is a diameter of the circle and B is a point on the circle. ACD is [#permalink]

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New post 20 Oct 2017, 21:08
(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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Re: AC is a diameter of the circle and B is a point on the circle. ACD is [#permalink]

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New post 23 Oct 2017, 18:02
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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Re: AC is a diameter of the circle and B is a point on the circle. ACD is   [#permalink] 23 Oct 2017, 18:02
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