Middle School

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The figure below shows concentric circles, both centered at 0.0

• Chord XY is tangent to the smaller circle

• The radius of the larger circle is 15cm

• The radius of the smaller circle is 12cm.

What is the length of chord XY?

A. 27 cm

B. 24cm

C. 18cm

D. 10cm

The figure below shows concentric circles both centered at 0 0 Chord XY is tangent to the smaller circle The radius of the larger circle

Answer :

Answer:

C. 18 cm

Step-by-step explanation:

The ratio of the sides of the triangle shown is 12 : 15 = 4 : 5. We know it is a right triangle, so we know the missing side length completes the ratio

3 : 4 : 5 = 9 : 12 : 15

Half of XY is 9 cm, so the length of the entire chord is 18 cm.

_____

The chord is tangent to the inner circle, so makes a 90° angle with the radius to that tangent point. This tells you that the triangle shown is a right triangle. It also tells you that the short radius bisects the chord. The Pythagorean theorem can be used to find the length of the side not shown (half the chord length).

The unknown side (a) can be found from ...

15² = 12² +a²

225 -144 = a² . . . . . . subtract 12²

81 = a² . . . . . . . . . . . simplify

9 = a . . . . . . . . . . . . . take the square root

The chord length is 2a, so is ...

2(9 cm) = 18 cm . . . . length of chord XY

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Rewritten by : Barada