SOLUTION: If the lengths of the bases of an isosceles trapezoid inscribed in a circle are 10 cm and 22 cm, and if one of the legs is 10 cm, then what is the length of a diagonal, in cm?

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Question 1150801: If the lengths of the bases of an isosceles trapezoid inscribed in a circle are 10 cm and 22 cm, and if one of the legs is 10 cm, then what is the length of a diagonal, in cm?
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Make a sketch.


Let ABCD be the given isosceles trapezoid.
The bases are AB = 22 cm long;  CD = 10 cm;
the lateral sides are AD = BC = 10 cm.






Draw the perpendiculars CE and DF from the vertices C  and D to the base AB.

It is clear that the right-angled triangles ADF  and BCE are congruent.

Then the segments AF and BE have the length   =  =  = 6 cm each.


The height of the trapezoid CE is the leg of the right angled triangle BCE and its length is equal to   =  =  = 8 cm.


Now from the right-angled triangle AEC you have

    AC =  =  =  =  =  =  = .


Thus the diagonal of the trapezoid AC is   cm long.   ANSWER



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