SOLUTION: In a circle with radius 4 cm the diameters AC and BD are perpendicular to each other. Prove that ABCD is a square. Find the area of ABCD. Include formal proof as well!!

Algebra ->  Rectangles -> SOLUTION: In a circle with radius 4 cm the diameters AC and BD are perpendicular to each other. Prove that ABCD is a square. Find the area of ABCD. Include formal proof as well!!      Log On


   

Question 1028626: In a circle with radius 4 cm the diameters AC and BD are perpendicular to each other. Prove that ABCD is a square. Find the area of ABCD.
Include formal proof as well!!
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!


Angles A,B,C,D are all 90 degrees as they are all angles subtended in a semicircle O is the centre of the circle
In Triangles ABC ADC
angle B = angle D
AC is the common side
and AO = DO
Therefore triangles are congruent
Therefore AB = AD
Adjacent sides are equal and are 90 deg.
Hence ABCD is a square