A B C are three points on the circumference of a circle and if AB AC 5 radic 2 cm and ang BAC 90 deg...........

Quantitative Aptitude ( CCS) Geometry

Download Solution PDF

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.

10 cm

5 cm

20 cm

15 cm

छोटे Courses बड़े Results

Master Geometry

Prepare through Micro-courses

Try Now

Explanation:

AB = AC = 5√2 cm, ∠BAC = 90°
Note : The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∴ Exterior ∠BOC = 2 × ∠BAC = 2 × 90° = 180°
∴ ∠BOC = 360° – Exterior ∠BOC = 360° – 180° = 180°
OA = OB = OC = r cm (radii)
AB = AC
∴ ∠AOB = ∠AOC = 90°
In ΔAOB, By pythagoras theorem
AB² = OA² + OB²
(5√2)² = r² + r²