If AB = 3cm, AC = 4cm, ad = 2.5cm, find the radius of circle o

If AB = 3cm, AC = 4cm, ad = 2.5cm, find the radius of circle o


In the right triangle abd, from ab = 3, ad = 2.5, we get that,
sin∠B=AD/AB=2.5/3=5/6
In △ ABC, from the sine theorem, we get
AC/sin∠B=2r,
That is 4 / (5 / 6) = 2R
The solution is r = 12 / 5



Triangle ABC is inscribed in circle O, and ab = AC = 5cm, BC = 6cm, find the radius of circle o


OA=OB=R
Let the midpoint of BC be d
OD=X
AD=4
X+R=4
X^2+9=R^2
X=7/8
R=25/8