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Circle A and circle B are congruent. CD is a chord of both circles. If CD = 16 cm and the radius is 17 cm, how long is AB?

A. 30 cm
B. 15 cm
C. 23 cm
D. 12 cm

Circle A and circle B are congruent. CD is a chord of both circles. If CD = 16 cm-example-1
User Alextunyk
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1 Answer

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The answer is A. 30 cm. CD and AB both intersect creating a right angle which I have indicated with a purple pen. According to the info you gave me, the radius is 17 so the line in red connecting point A and point C is 17 as that's a radius. Because the lines form a right triangle, you can use Pythagorean theorem to solve for the missing length. so if CD is 16, half of that is 8. 17 squared minus 8 squared is 225. Find the square root which gives you 15. 15 is only HALF the length of AB so you'd have to basically repeat to the other side (which is basically a waste of time so just multiply 15 by 2) and BOOOOOOOM. A. 30 cm. : ) hope i helped.
Circle A and circle B are congruent. CD is a chord of both circles. If CD = 16 cm-example-1
User Vbullinger
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7.8k points

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