An isoscelless triangle of sides of 13cm, 13cm, 10cm is inscribed in a circle is inscribed in a circle. What is the radius of the circle?

Answer 1

draw radii from center to the three intersections on the circumference
all length r
sine of half angle up at intersection of 13 cm legs = 5/13
so half angle = 22.6 deg

isosceles triangle now with legs r meeting base 13 at 22.6 angle
cos 22.6 = r/6.5

r = 6.5 cos 22.6
r = 6

Answer 2

From the diagram
Sin<=5/13=0.3846
<=22.6
22.6*2=45.2(< at centre=2 times< at circumference
sin45.2=5/r
r=7.04cm