Problem:
A circle passes through the three vertices of an isosceles triangle that has two sides of length 3 and a base of length 2. What is the area of this circle?
Answer Choices:
A. 2Ï€
B. 25​π
C. 3281​π
D. 3Ï€
E. 27​π
Solution:
Let BD be an altitude of the isosceles â–³ABC, and let O denote the center of the circle with radius r that passes through A,B, and C, as shown.
Then
BD=32−12​=22​ and OD=22​−r
Since â–³ADO is a right triangle, we have
r2=12+(22​−r)2=1+8−42​r+r2, and r=42​9​=89​2​
