Math CentralQuandaries & Queries


Question from Bob, a student:

A circle is insubscribed in an isosceles trapezoid, with parallel lengths of 8cm and 18cm.
What is the lengths of sloping edges and why?


If the inscribed circle with center O touches ABCD at W (on AB), X(on BC), Y(on CD) and Z (on DA), then triangles OAW, OAZ are congruent (why?) as are three other pairs. [Draw and label the diagram]

So AW = AZ [and three other equalities - find them!]

Deduce from this that AB + CD = BC + AD for any quadrilateral with an inscribed circle. (Less obviously, this is if-and-only-if.)

Solve your problem.

Good hunting!

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS