Problem:
Quadrilateral ABCD is inscribed in a circle with ∠BAC=70∘,∠ADB=40∘, AD=4, and BC=6. What is AC ?
Answer Choices:
A. 3+5
B. 6
C. 292
D. 8−2
E. 7
Solution:
Because ∠BAC and ∠BDC intercept the same arc, ∠BDC= 70∘. Then ∠ADC=110∘ and ∠ABC=180∘−∠ADC=70∘. Thus △ABC is isosceles, and therefore AC=BC=6.
The problems on this page are the property of the MAA's American Mathematics Competitions