SOLUTION: O is the centre of the circle,points ABCD are in the circle (hence, ABC are points of triangle) OD is the perpendicular bisector of BC. Prove that AD is the angle bisector of A.

Algebra ->  Geometry-proofs -> SOLUTION: O is the centre of the circle,points ABCD are in the circle (hence, ABC are points of triangle) OD is the perpendicular bisector of BC. Prove that AD is the angle bisector of A.      Log On


   

Question 252894: O is the centre of the circle,points ABCD are in the circle (hence, ABC are points of triangle)
OD is the perpendicular bisector of BC.
Prove that AD is the angle bisector of A.
Im not to sure how start this question and how to write out the proof?
thank you for looking
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

You asked how to START so here is how to start.
The first thing is to draw the circle with center O on graph paper.
for ease make the center the origin (0,0)
Then draw the triangle ABC. Then draw OD so that it bisects BC such that the point where OD and BC cross is in the middle of BC.
Now draw AD and notice whether it looks like it is bisecting the angle BAC.
mark all the lines from the origin to the edge of the circle as equal since they are all radiuses (radii) of the circle (OC, OA and OB) BD and BC are also equal
so we have two triangles ADC and ADB with two known sides to be equal
AD is common to both triangles and so of course is equal in both triangles and the as was said above BD and BC are equal (Do you know why? They are hypotenuses of triangles where the legs are equal)
You should be able to see where I am going by now.