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Question : A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. The radius of the circle is:

Option 1: 13 cm

Option 2: 12 cm

Option 3: 16 cm

Option 4: 15 cm


Team Careers360 8th Jan, 2024
Answer (1)
Team Careers360 13th Jan, 2024

Correct Answer: 13 cm


Solution :
Let O be the centre of the circle.
Let AB be the chord of length 24 cm
Let OD be perpendicular from the centre to the chord AB of length 5 cm.
We know the perpendicular from the centre to a chord bisects the chord.
So, AD = BD = 12 units
Applying Pythagoras theorem in triangle OBD,
OB 2 = OD 2 + DB 2
⇒ OB 2 = 5 2 + 12 2
⇒ OB 2 = 169
⇒ OB = 13
Hence, the correct answer is 13 cm.

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