A, B, C, are three points on the circumference of a circle and if $AB=AC=5\sqrt{2}$, $∠BAC=90°$ then radius of the circle is ______.

5 cm

AB = AC = 5√2 cm

∠BAC = 90º

Pythagoras theorem

We know that,

If, In ΔABC, ∠A = 90° 

BC² = AB² + AC²

The diameter of circle subtent right angles at any point on the circumference of the circle.

∠A = 90° 

So, We can say that BC is a diameter of circle

Now, AB = AC = 5√2 cm and ∠BAC = 90º,

In right angle ∆ BAC

By using Pythagoras theorem:

⇒ BC² = AB² + AC²

⇒ BC² = (5√2)² + (5√2)²

⇒ BC² = 50 + 50

⇒ BC² = 100

⇒ BC = 10 cm

⇒ BC is the diameter of the circle

⇒ Radius of the circle = 10/2 = 5 cm