Prove that quadrilateral ABCD is cyclic if diagonal AC is perpendicular to side BC and diagonal BD is perpendicular to side AD.
Need a hint to start...I'm stuck with this...
Thanks in advance!
Hello, logan6!
Prove that quadrilateral ABCD is cyclic
if diagonal and diagonalCode:D * * C o- - - - - - -o * / * * \ * * / * \ * / * * \ */ * * \* A o - - - - - - - - - - - o B
Then right triangle is inscribed in semicircle
Then right triangle is inscribed in semicircle
Hence, quadrilateral is inscribed in semicircle
Therefore: .quadrilateral is cyclic.
Thank you very much! You made my bulb glow!
Note: I made a petite modification. I hope you don't mind.
Then right triangle is inscribed in circle ACB. (r=AB/2, center in the middle of hypotenuse AB)
Then right triangle is inscribed in circle ADB. (r=AB/2, center in the middle of hypotenuse AB))
Hence, quadrilateral is inscribed in circle
Therefore: .quadrilateral is cyclic.