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.

Daniel Chiu by Daniel Chiu , 22, USA

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1 solution

Ahmad Saad
Mar 12, 2017

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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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