A, B, C are three points on the circumference of a circle

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A, B, C are three points on the circumference of a circle and if AB = AC = 5√2 cm and ∠BAC = 90°, find the radius.

1. 10 cm
2. 5 cm
3. 20 cm
4. 15 cm

Correct Option: B

As per the given in question , we draw a figure a circle in which A, B, C are three points on the circumference ,

In ∆s OAB and OCA,
OC = OA = OB = radii
2 ∠ OAB + ∠ AOB = 180°
2 ∠ OAC + ∠ AOC = 180°
∴ ∠ AOB + ∠ AOC = 360° – 2 (∠ OAB + ∠ OAC)
∠ AOB + ∠ AOC = 360° – 2 × 90° = 180°
AB = AC
∴ ∠ AOB = 90°
∠ OAB = 45°

⇒ sin OAB =	OB
	AB

⇒ sin 45° =	OB
	5√2

⇒ OB = 5 √2.sin 45°

OB = 5 √2 ×	1	= 5cm.
	√2