document.write( "Question 33829: This is on Ptolemy's theorem. If CD =1, BC = 2, AD = 3, AB = 4, and the triangle ADC is a right triangle, can the quadrilateral ABCD be inscribed in a circle?\r
\n" ); document.write( "\n" ); document.write( "Yes or No \n" ); document.write( "

Algebra.Com's Answer #20225 by venugopalramana(3286) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is on Ptolemy's theorem. If CD =1, BC = 2, AD = 3, AB = 4, and the triangle ADC is a right triangle, can the quadrilateral ABCD be inscribed in a circle?
\n" ); document.write( "TO USE PTOLEMYS THEOREM YOU NEED AC AND BD AND CHECK IF
\n" ); document.write( "AB*CD+AD*BC=AC*BD...IF YES IT IS CYCLIC QUADRILATERAL OTHERWISE NOT..HERE WE CAN FIND AC..BUT BD NEEDS CALCULATION..SO I AM GIVING ANOTHER WAY TO DO IT FROM PROPERTY OF CYCLIC QUADRILATERAL THAT SUM OF OPPOSITE ANGLES=180
\n" ); document.write( "ADC IS RIGHT TRIANGLE...ANGLE D=90...SO....AC^2=AD^2+DC^2=3^2+1^2=10
\n" ); document.write( "WE FIND THAT IN TRIANGLE ABC
\n" ); document.write( "AB^2+BC^2=4^2+2^2=20 WHICH IS NOT EQUAL TO AC^2...HENCE ABC IS NOT A RIGHT TRIANGLE.HENCE ANGLE B IS NOT 90.
\n" ); document.write( "HENCE SUM OF OPPOSITE ANGLES ADC AND ABC IS NOT 180..HENCE ABCD IS NOT A CYCLIC QUADRILATERAL... \n" ); document.write( "

\n" );