jmc

Question

Three congruent isosceles triangles DAO, AOB, and OBC have AD=AO=OB=BC=10 and AB=DO=OC=12. These triangles are arranged to form trapezoid ABCD, as shown. Point P is on side AB so that OP is perpendicular to AB. FIGURE What is the length of OP?

Accepted Answer

Since AOB is isosceles with AO=OB and OP is perpendicular to AB, then P is the midpoint of AB, so AP=PB=12AB=12(12)=6. By the Pythagorean Theorem, OP = AO^2 - AP^2, so we have OP = 10^2-6^2=64=8.