Tammy has a circular garden with a diameter of 36 feet. She will create 4 stone
pathways in the garden that will form an inscribed quadrilateral in her circular
garden. Tammy wants the straight-line distance between one pair of opposite
vertices to be 36 feet. She also wants two consecutive pathways to have
lengths of 24 feet and 12 feet. Tammy will plant marigolds along the shorter edge of
the garden that is cutoff by the pathways of lengths 24 feet and 12 feet.
What length, to the nearest tenth of a foot, of the edge of the garden will be planted
with marigolds?
Consider the quadrilateral ABCD: let's draw AC - it will be perpendicular to the side AB, due to the property of an inscribed angle that relies on the diameter. Proceeding from this, the triangle ABD is right-angled, then:
;
Behind the property of the angles of a quadrilateral inscribed in a circle:
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