Archive
29th of March 2017
Mathematics
Q:

Bisector AD of angle BAC of triangle ABC passes through centre O of circumcircle of triangle.Prove that AB=AC

Vikas Mahajan - CBSE - Class IX

Wednesday, March 29, 2017 at 17:48:PM

A:

begin mathsize 16px style Since space AD space is space the space bisector comma
so space angle OAB equals angle OAC space space.... left parenthesis straight i right parenthesis
OA equals OB equals OC space left parenthesis since space radii space of space the space same space circle right parenthesis
rightwards double arrow angle OAB equals angle OBA space.... left parenthesis ii right parenthesis
and space angle OAC equals angle OCA space space.... left parenthesis iii right parenthesis
and space angle OBC equals angle OCB space space.... left parenthesis iv right parenthesis
From space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis comma space left parenthesis iii right parenthesis space and space left parenthesis iv right parenthesis comma space we space get
angle OAB equals angle OBA equals space angle OAC equals angle OCA
Now comma
angle ABD equals angle OBA plus angle OBC
rightwards double arrow angle ABD equals angle OCA plus angle OCB
rightwards double arrow angle ABD equals angle ACD
space rightwards double arrow AB equals AC space space space space space space space space space space

end style

Wednesday, March 29, 2017 at 18:01:PM