Question:
On a semicircle with diameter AD, chord BC is parallel to the diameter. Further; AD and BC are separated by 2cm, while AD has length 8. What is the length of BC?
On a semicircle with diameter AD, chord BC is parallel to the diameter. Further; AD and BC are separated by 2cm, while AD has length 8. What is the length of BC?
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The semicircle has radius 4 and centre at the midpoint of AD. Use Pythagoras with the perpendicular distance 2 to the chord.
Updated On: Nov 4, 2026
- \( 2\sqrt{3} \)
- \( 4\sqrt{3} \)
- 8.6
- None of the above
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Set up:
AD = 8, so the radius is 4 and the centre O is the midpoint of AD. Chord BC is parallel to AD at perpendicular distance 2 cm from it.
Step 2: Half chord:
Let M be the midpoint of BC. OM = 2 (perpendicular distance), OB = 4. So \( BM=\sqrt{4^2-2^2}=\sqrt{12}=2\sqrt3 \).
Step 3: Length of BC:
\( BC=2\cdot2\sqrt3=4\sqrt3 \) cm \( \approx 6.93 \) cm.
Final Answer:
The correct option is (2): \( 4\sqrt{3} \)
AD = 8, so the radius is 4 and the centre O is the midpoint of AD. Chord BC is parallel to AD at perpendicular distance 2 cm from it.
Step 2: Half chord:
Let M be the midpoint of BC. OM = 2 (perpendicular distance), OB = 4. So \( BM=\sqrt{4^2-2^2}=\sqrt{12}=2\sqrt3 \).
Step 3: Length of BC:
\( BC=2\cdot2\sqrt3=4\sqrt3 \) cm \( \approx 6.93 \) cm.
Final Answer:
The correct option is (2): \( 4\sqrt{3} \)
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