Three consecutive sides of a quadrilateral circumscribed about a circle are 1: 2: 3. Find the fourth number in this regard?

univerkov | May 15, 2021 | education

Since a circle is inscribed in a quadrilateral, the sums of the lengths of the opposite sides of such a quadrilateral are equal.

AB + CD = BC + AD.

Let the length of the segment AB = X cm, then BC = 2 * X cm, CD = 3 * X cm.

AB + CD = X + 3 * X = 4 * X cm.

Then BC + AD = 4 * X = 2 * X + AD.

AD = 4 * X – 2 * X = 2 * X cm.

Then the ratio of the sides of the quadrilateral is 1/2/3/2.

Answer: The aspect ratio is 1/2/3/2.

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