Inside the circle, a point is given at a distance of 15 cm from the center, a chord is drawn through this point

| September 3, 2021 | education

Inside the circle, a point is given at a distance of 15 cm from the center, a chord is drawn through this point, which is divided by it into two parts 7 cm and 25 cm long. Find the radius of the circle.

Let the length of the segment CB = X cm, then the radius of the circle will be equal to: R = (15 + X) cm, and the length of the segment EC = (15 + X + 15) = (30 + X) cm.

Chords AD and BE intersecting, then by their property, the product of the lengths of the segments formed at the intersection of one chord is equal to the product of the lengths of the segments of the other chord.

AC * DS = BC * EA.

7 * 25 = X * (30 + X).

X2 + 30 * X – 175 = 0.

Let’s solve the quadratic equation.

X1 = 5.

X2 = -35. (Inappropriate, since it is less than zero).

Then R = 15 + 5 = 20 cm.

Answer: The radius of the circle is 20 cm.



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