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 ______.
Answer & explanation
Correct answer: option 2
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