Question

'O' is the centre of a circle and AB is the diameter
Chord AC = 48 cm. and Chord BC = 14 cm. then
fnd the radius of the circle.
a) 50 cm.
b) 25 cm.
c) 60 cm
d) 35 cm
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Answer 1

QUESTION

'O' is the centre of a circle and AB is the diameter  Chord AC = 48 cm. and Chord BC = 14 cm. then

fnd the radius of the circle.

ANSWER

AB = 6 cm, OD = 4 cm and O is the center of the circle.

AB is a chord and OD is perpendicular to AB.

OA = Radius = ?

It is clear from the figure that AD = DB = 1/2 of AD

⇒ 1/2 × 6

⇒ AD = 3 cm

Now, using Pythagoras Theorem -  

⇒ (Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ (OA)² = (AD) + (OD)²

⇒ (OA)² = (3)² + (4)²

⇒ (OA)² = 9 + 16

⇒ (OA)² = 25

⇒ OA = √25

⇒ OA = 5 cm

So, the radius of the circle is 5 cm