Two parallel chords in the same circle have lengths of 30cm and 48 cm. The circle has a radius of 25 cm. How far apart are the chords?

Question

anonymous · Answer

would the answer be $$\approx 11?$$

anonymous · Answer

umm what were ur steps?

anonymous · Answer

I'm not sure....

anonymous · Answer

BA is the chord of length 30 cm and P is its midpoint. Triangle APC is a right triangle, the length of CA is 25 cm and the length of AP is 30/2 = 15 cm.

anonymous · Answer

hadn't thought thay they could be on the same side of the radius..
And the textbook doesn't specify.
I know the answers are in the back, but they don't have processes to find them.

dumbcow · Answer

They are 13 cm apart

directrix · Answer

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Distance is perpendicular distance. The perpendicular to a chord bisects the chord. In each case, we get right triangles.

Pythagorean Triples come in handy as (15, 20, 25) is a 5 multiple of the (3,4,5) triple and (7, 24,25) is a primitive triple.

Regardless, the Pythagorean Theorem can be used: 25^2 = 15^2 + h^2 where h = 20 and then again as 25^2 = 24^2 + d^2 and d = 7. 

7 + 20 = 27 for the distance between the parallel chords.