Question

ABC is an isosceles triangle inscribed in a circle.If AB=AC=25cm and BC=14cm find the radius of the circle.

Answer 1

Draw AD⊥BC
Hence D is the midpoint of BC
That is BD = DC = (1/2) BC
Therefore, BD = DC = 7 cm
In right triangle ADB, by Pythagoras theorem we have
AB2 = AD2 + BD2
252 = AD2 + 72
625 = AD2 + 49
AD2 = 576
Therefore, AD = 24 cm
Consider, right triangle ODB, by Pythagoras theorem we have
OB2 = OD2 + BD2
Here OD = AD – AO = 24 – r, where r is radius of the circle
r2 = (24 – r)2 + 72
Simplify to get the value of r