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Point  is 9 units from the center of a circle of radius 15. How many different chords of the circle contain  and have integer lengths?

 Oct 14, 2022
 #1
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The answer is 28.

 Oct 14, 2022
 #2
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 How many different chords of the circle contain and have integer lengths?

 

Hello Guest!

 

The largest chord is diameter 30. Your sections are 6 and 24.

The product of the respective chord sections is constant (tendon law).

The product of all chord segments is 144.

144 = 6 * 24,     6 + 24 = 30 This is the largest chord.

144 = 8 * 18,     8 + 18 = 26

144 = 9 * 16,     9 + 16 = 25

144 = 12 * 12, 12 + 12 = 24 This is the smallest chord.

 

Four different chords with integer length are possible.

laugh  !

 Oct 14, 2022
edited by asinus  Oct 14, 2022
edited by asinus  Oct 14, 2022

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