Find the chord length of a circle with a radius of 13 cm if the distance from the center of the circle to the chord is 5 cm.

Darius Nash 2022-09-12 Answered
Find the chord length of a circle with a radius of 13 cm if the distance from the center of the circle to the chord is 5 cm.
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Answers (1)

Duncan Kaufman
Answered 2022-09-13 Author has 17 answers
AB is the chord, O is the center of the circle, OH is the distance from the center to the chord.The distance from a point to a straight line is the length of the perpendicular drawn from this point to the straight line, which means OH is the height of the triangle AOB.
Tr-nick AOB is isosceles, AO = OB as the radii of a circle, AB is the base. In an isosceles tr-ke, the height drawn to the base is also the median, which means AH = BH.
Since VN is the height, the ANO tr-nick is rectangular. By the Pyfaror theorem, we find the leg AN:
A H = 13 2 5 2 = 169 25 = 144 = 12 ( c m )
AB=12*2=24(cm)
Answer: 24cm

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