An isosceles triangle is inscribed in a circle of radius 5 t

An isosceles triangle is inscribed in a circle of radius 5. two sides of the triangle have length 4. what is the length of the third side?

Solution

Let length of the base = z

Let the distance from apex of the triangle to the base of the triangle = x

and given the radius = 5,

As, the triangle is iscosceles, a perpendicular fgrom the apex to the base passes through the centre of the circle.

Distance from centre of the circle to the base = 5 - x

By Pythagoras Theorom,

x ² + z² = 16 and (5-x)² + z² = 25

Solving the above two equations

x = 1.6 and z = 3.67

So the length of the third side or the base = 2 * 3.67 = 7.34