The diameter of a circle is 50. The distance if chord from the circle is 7. Find the length of the chord
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48 will be answer chord will be 48
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The chord, AB, forms an isosceles triangle at the center (O) of the circle.
The diameter (CD) being 50 cm the radius (OA = OB) of the circle is 25 cm.
The mid point of the chord AB is say P. POA and POB are right angle triangles, whose hypotenuse is 25 cm and the distance OP = 7 cm. Then from Pythagoras formula (in triangle POA)
OA^2 = OP^2+AP^2, or
25^2 = 7^2 + AP^2 , or
AP^2 = 25^2–7^2 = 625–49 = 576, or
AP = 576^0.5 = 24 cm
So the chord AB = 2*AP = 2*24 = 48 cm.
The diameter (CD) being 50 cm the radius (OA = OB) of the circle is 25 cm.
The mid point of the chord AB is say P. POA and POB are right angle triangles, whose hypotenuse is 25 cm and the distance OP = 7 cm. Then from Pythagoras formula (in triangle POA)
OA^2 = OP^2+AP^2, or
25^2 = 7^2 + AP^2 , or
AP^2 = 25^2–7^2 = 625–49 = 576, or
AP = 576^0.5 = 24 cm
So the chord AB = 2*AP = 2*24 = 48 cm.
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