Question

A chord of length 8 cm is drawn at a distance
of 3 cm from the centre of a circle. Calculate
the radius of the circle.​

Answer 1

Step-by-step explanation:

by Pythagoras theorem,

height= 3cm

base = 8/2 = 4cm ............ (perpendicular bisector)

hypotenuse = radius = ?

so,

$({hypoteneus})^{2} = ( {base})^{2} + ( {height)}^{2} \\ = {4}^{2} + {3}^{2} \\ = 16 + 9 \\ = \sqrt{25} \\ = 5cm$

radius = 5cm

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Answer 2

AB is the chord of a circle with center O

And radius OA and OM ⊥ AB

AB = 8 cm

OM = 3 cm

OM ⊥ AB

M is the mid-point of AB

AM = ½ AB = ½ × 8 = 4 cm.

Now in right ∆OAM

OA² = OM² + AM²

(By Pythagoras Axiom)

= (3)² + (4)² = 9 + 16 = 25

= (5)²

OA = 5 cm.

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