The chords ab and cd meet at point e. find ed if AE = 0.2 BE = 0.5, CD = 0.65

By the property of intersecting chords, the product of the segments formed at the intersection of one chord is equal to the intersection of the segments of the other chord.

AE * BE = CE * DE.

Let the length of the segment DE = X cm, then CE = (CD – DE) = (0.65 – X) cm.

0.2 * 0.5 = (0.65 – X) * X.

0.1 = 0.65 * X – X ^ 2.

X ^ 2 – 0.65 * X + 0.1 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = (-0.65) ^ 2 – 4 * 1 * 0.1 = 0.4225 – 0.4 = 0.0225.

X1 = (0.65 – √0.0225) / (2 * 1) = (0.65 – 0.15) / 2 = 0.5 / 2 = 0.25.

X2 = (0.65 + √0.0225) / (2 * 1) = (0.65 + 0.15) / 2 = 0.8 / 2 = 0.4.

Answer: The length of the unit segment is 0.25 cm or 0.4 cm.

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