A, B and C are three points on the circle. If AB = AC = $7\sqrt{2}$ cm and ∠BAC = 90°, then the radius is equal to :

7 cm

We know that,

(Hypotenius)² = (pependicular)² + (base)²

We have,

AB = AC = 7\(\sqrt {2}\) cm

Radius = \(\frac{ diameter }{2}\)

∠ A = 90⁰

(AB)² + (AC)² = (BC)²

(7\(\sqrt {2}\))² + (7\(\sqrt {2}\))² = (BC)²

= 98 + 98 = (BC)²

⇒ (BC)² = 196

= BC = 14

BC = diameter

So, radius = \(\frac{14}{2}\) = 7 cm