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 :
Answer & explanation
Correct answer: option 2
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