An isosceles triangle of sides 13cm, 13cm, 10cm is inscribed in a circle. What is the radius of the circle?
A.
7cm
B.
12cm
C.
8cm
D.
36cm
E.
69cm
Correct answer is A
In \(\Delta DAC, \stackrel\frown{DAC} = \theta\)
\(\sin \theta = \frac{5}{13}\)
\(\theta = 22.6°\)
\(< DOC = 22.6° \times 2 = 45.2°\)
\(\sin 45.2 = \frac{5}{r} \implies r = \frac{5}{\sin 45.2}\)
\(r = 7.046cm\)
= \(7\frac{1}{24} cm\)