130 views

ABCD is a quadrilateral. Point O is along AD. A semicircle has a diameter along AD and is tangent to the sides AB, BC, and CD. If AB = 9, CD = 16, and AO = OD, what is the length of AD?

posted Jan 6, 2021
Looking for solution? Promote on:

Similar Puzzles

Semicircle AB is flipped upside down and translated horizontally so the new semicircle CD is tangent to AB, as shown. The line through AB is tangent to the semicircle CD and the line through CD is tangent to the semicircle AB.

If each semicircle has a diameter equal to 2, what is the length of AD?
Express your answer in the form √x + √y for positive integers x < y.

+1 vote

Quadrilateral ABCD has AD = BC, ∠A + ∠B = 90°, AB = 20, CD = 10, as shown below.

What is the area of ABCD?

+1 vote

A semicircle with radius a is inscribed in a rectangle with its diameter along one side of the rectangle. A circle with radius b is then inscribed so it is tangent to the rectangle and the semicircle, as shown.
Solve for the value of a/b.