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Quadrilateral ABCD is inscribed into a circle. What is the [#permalink]
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
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.