SOLUTION: The radius of the circle is 17 m. The radius CD is perpendicular to the chord AB. Their point of intersection, E, is 8 m from the center C. What is the length of the chord AB?

Algebra ->  Circles -> SOLUTION: The radius of the circle is 17 m. The radius CD is perpendicular to the chord AB. Their point of intersection, E, is 8 m from the center C. What is the length of the chord AB?       Log On


   

Question 1153751: The radius of the circle is 17 m. The radius
CD is perpendicular to the chord AB. Their
point of intersection, E, is 8 m from the
center C. What is the length of the chord
AB?
Found 3 solutions by ikleyn, greenestamps, MathLover1:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

Make a sketch and apply the Pythagorean theorem to right angled triangle CDA


   the length of AD = sqrt%2817%5E2-8%5E2%29 = sqrt%28289-64%29 = sqrt%28225%29 = 15.


Hence, the length of AB is twice this length, i.e.  AB = 2*15 = 30 meters.    ANSWER

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I think that EVERYBODY and EVERYONE is able to solve it on his or her own, under one indispensable condition:
he or she should make his or her first step producing a sketch.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!
The radius CD is perpendicular to chord AB, so it bisects the chord.

Draw the radius CA; that forms right triangle CEA in which the lengths of the hypotenuse and one leg are known. Use the Pythagorean Theorem to find the length of the other leg.

That other leg is half the length of the chord, so double the length of that leg to find the length of the chord.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

CD=17m
CD is perpendicular to the chord AB
EC=8m+
first sketch it:


from right triangle CEB, using Pythagorean theorem, we have
%28AB%2F2%29%5E2=%2817m%29%5E2-%288m%29%5E2
%28AB%2F2%29%5E2=289m%5E2-64m%5E2
%28AB%2F2%29%5E2=225m%5E2
AB%2F2=sqrt%28225m%5E2%29
AB%2F2=15m
AB=15m%2A2
AB=30m
the length of the chord AB is 30m