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:
⇒ [tex]Hypotenuse^{2} = Base^{2} + Perpendicular^{2}[/tex]
⇒ [tex]13^{2} = 5^{2} + Perpendicular^{2}[/tex]
⇒ [tex]Perpendicular^{2} = 13^{2} - 5^{2}[/tex]
⇒ [tex]Perpendicular^{2} = 169} - 25}[/tex]
⇒ [tex]Perpendicular^{2} = 144[/tex]
⇒ [tex]Perpendicular^{2} = \sqrt{144}[/tex]
⇒ [tex]Perpendicular = 12[/tex]
∴ Length AC is 12 .
