A chord of length 16 units lies in a circle of radius 10 units. How far is the chord from the centre?
A8 units
B4 units
C2 units
D6 units
Answer & Solution
Correct answer: D. 6 units
1. Draw the line from the centre perpendicular to the chord.
2. That line bisects the chord, so each half is 16 divided by 2, which is 8 units.
3. Now draw a radius to one end of the chord to make a right-angled triangle.
4. The radius of 10 units is the hypotenuse, and one short side is the half chord of 8 units.
5. By the theorem of Pythagoras, the square of the hypotenuse is the sum of the squares of the other two sides.
6. So 10 times 10 is 100, and 8 times 8 is 64, leaving 100 minus 64, which is 36.
7. The distance from the centre is the number whose square is 36, which is 6 units.
8. Answering 8 units gives the half chord rather than the distance from the centre.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 8: Euclidean geometry_
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