Question : A 15 cm long perpendicular is drawn from the centre of a circle to its 40 cm long chord. Find the radius of the circle.
Option 1: 25 cm
Option 2: 27 cm
Option 3: 22 cm
Option 4: 20 cm
Correct Answer: 25 cm
Solution :
Given: Chord length = 40 cm
The perpendicular distance from centre to chord = 15 cm
Let the chord be AB and R be the radius of the circle.
Since a perpendicular from the centre divides a chord into two equal parts, AP = 20 cm
In $\triangle$OAP
Using Pythagoras' theorem: OA
2
= OP
2
+ PA
2
.
R
2
= 15
2
+ 20
2
⇒ R
2
= 225 + 400 = 625
⇒ R = 25
Hence, the correct answer is 25 cm.
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