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Quadrilateral ABCD is inscribed into a circle. What is the

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Senior Manager
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Quadrilateral ABCD is inscribed into a circle. What is the [#permalink] New post 29 Oct 2008, 22:57
Quadrilateral ABCD is inscribed into a circle. What is the value of \angle BAD ?

1. AC = CD
2. \angle ADC = 70^o

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient


Does that symbol signify arch?
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Re: Geometry [#permalink] New post 29 Oct 2008, 23:18
E. From the two statements, we only know of A, C and D. Nothing is known for B. Hence, angle BAD can be anything.

P.S. I assumed the symbol represents angle.
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Re: Geometry [#permalink] New post 30 Oct 2008, 01:32
I'd go for E as well, but let's tackle the problem in more depth.

A quadrilateral can be inscribed into a circle only when the sum of its opposite angles is 180.
So, A+C=B+D=180 => A=180-C
We need to know C in order to find the value of A.

1) AC=CD: From this we know the ACD is an isosceles triangle, then the angles CDA and DAC are equal, but we do not have any information about C => INSUFFICIENT.

2) ADC=70: this means that angle B=110. Again, we don't know the value of C => INSUFFICIENT.

If we combine stmts 1&2, we get that angle DCA=40 (since it's DCA=180-70-70). But once again, this isn't enough to understand the value of the complete angle in C => E, stmts 1&2 together are not sufficient.

OA?
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Re: Geometry [#permalink] New post 30 Oct 2008, 10:32
what does than symbol mean, anyway :? Lengh of arc, or measure of an angle, or smth else?
Re: Geometry   [#permalink] 30 Oct 2008, 10:32
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