Question

△ABC is inscribed in a circle such that vertices A and B lie on a diameter of the circle. If the length of the diameter of the circle is 13 and the length of chord BC is 5, find length AC.
The length AC is

Answer 1

Length AC is 12 .

Step-by-step explanation:

We have , △ABC is inscribed in a circle such that vertices A and B lie on a diameter of the circle. If the length of the diameter of the circle is 13 and the length of chord BC is 5 . According to the data given in question we can visualize that triangle must be a right angled triangle where:

AB = hypotenuse = 13

BC = base = 5

Ac = Perpendicular

Now, By Pythagoras Theorem:

⇒ $Hypotenuse^{2} = Base^{2} + Perpendicular^{2}$

⇒ $13^{2} = 5^{2} + Perpendicular^{2}$

⇒ $Perpendicular^{2} = 13^{2} - 5^{2}$

⇒ $Perpendicular^{2} = 169} - 25}$

⇒ $Perpendicular^{2} = 144$

⇒ $Perpendicular^{2} = \sqrt{144}$

⇒ $Perpendicular = 12$

∴ Length AC is 12 .