Chords AB and CD intersect at point E so that AE = 3cm BE = 36cm CE = 9cm DE = 12cm. Find the smallest radius value.

univerkov | June 17, 2021 | education

Let us determine the lengths of the chords AB and CD.

AB = AE + BE = 3 + 36 = 39 cm.

CD = CE + DE = 9 + 12 = 21 cm.

The smallest radius of a circle with the obtained lengths of chords will be if the diameter of the circle coincides with a chord of more length.

D = AB = 39 cm.

Then Rmin = D / 2 = 39/2 = 19.5 cm.

Answer: The smallest value of the radius of the circle is 19.5 cm.

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