If AC = 5cm, BC = 12cm and the radius of the circumscribed circle is __ cm and m∠OAC = °.

Solution:

The problem statement can be represented by a diagram as shown below:

The triangle inscribed in the circle is a right angled triangle,

hence we can use the pythagorean theorem to find AB which is the hypotenuse in this case.

AB² = AC² + BC²

AB² = (12)² + (5)²

144 + 25 = 169

AB = √169 = 13

Radius of circumscribed circle = 13/2

= 6.5

Cos θ = 5/13

Hence θ is approximately 67°.

If AC = 5 cm, BC = 12 cm, and, the radius of the circumscribed circle is __ cm and m∠OAC = °.

Summary:

If AC = 5 cm, BC = 12 cm and the radius of the circumscribed circle is 6.5cm and m∠OAC = 67°.