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OA and OB are congruent. CD is a chord of both circles.2If a radius is 17 ft and CD = 16 ft, how long is AB?АB

OA And OB Are Congruent CD Is A Chord Of Both Circles2If A Radius Is 17 Ft And CD 16 Ft How Long Is ABАB class=

Sagot :

Given the circles' A and B

As shown: the circles are congruent

CD is a chord of both circles, CD = 16 ft

The radius of the circle = 17 ft

Hint: connect AC

The intersection between AB and CD is the point E

So, for the triangle ACE:

CD will be perpendicular to AB

So, the measure of the angle AEC = 90

AC = 17 ft, CE = 0.5 * 16 = 8

so, the length of AE will be calculated using the Pythagorean theorem:

[tex]AE=\sqrt[]{17^2-8^2}=\sqrt[]{289-64}=\sqrt[]{225}=15[/tex]

So, the length of AB will be two times the length of AE

So, AB = 2 * 15 = 30

so, the answer will be AB = 30 ft

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