Question

An isosceles triangle ABC has its vertices on a circle. If ab=13,bc=13 and ac=10,calculate the height bm of the triangle and the radius of the circle to the nearest whole number

Answer 1

Answer:

Place the circle in such a way that the midpoint of CA becomes the origin, and

B lies on the y-axis

by Pythagoras BO = 12 cm

so we have points A(5,0), B(0,12) and C(-5,0)

let the centre be (0,k) and the radius r

equation:

x^2 + (y-k)^2 = r^2

using (5,0) --> 25 + k^2 = r^2

using (0,12) -> 0 + (12-k)^2 = r^2

12-k = r

k = 12-r

in 25+k^2 = r^2

25 + (12-r)^2 = r^2

25 + 144 - 24r + r^2 = r^2

24r = 169

r = 169/24 = 7.04166

The radius is appr 7 cm