Trapezium in a circle

Level pending

Let A B C D ABCD be an isosceles trapezium with A D = B C AD=BC , and with parallel bases of length A B = 150 AB=150 and C D = 234 CD=234 . If the distance between A B \overline{AB} and C D \overline{CD} is 56 56 , find the circumradius of A B C D ABCD .

Details and assumptions

A trapezium has a pair of parallel sides.


The answer is 125.

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1 solution

Ahmad Saad
Mar 12, 2017

The circumcircle of ABCD is the same for triangle ADC, and with the given information the sides of the triangle ACD is easy to find (AD=70, AC=200, CD=234) through the Pythagorean theorem. Then the circumradius can be found by the formulae abc/(4*area of triangle)= 125

Sathvik Acharya - 4 years, 1 month ago

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