If the length of a chord, drawn at a distance of 21 cm from the centre of a circle, is 40 cm, then the radius (in cm) of the circle is:

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1)
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  1. 29
  2. 21
  3. 25
  4. 20

Answer (Detailed Solution Below)

Option 1 : 29
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Detailed Solution

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Given:

Chord = 40cm 

Distance from centre to chord = 21 cm

Concept:

The perpendicular drawn from the centre of the chord bisects the chord in two equal parts. 

Pythagoras Theorem:

OA2 = OD2 + AD2

Calculation:

Let AB be the chord of length 40 cm. 

⇒ OD be the perpendicular distance 

⇒ AO be the radius of the circle 

OA2 = OD2 + AD2

OA2 = 212 + (40/2)2

OA= 441 + 400 

⇒ OA2= 841

OA = √841

OA = 29

The radius (in cm) of the circle is 29.

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