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

CBSE Class 9 Answered

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

Asked by Vikas | 29 Mar, 2017, 05:48: PM

Expert Answer

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

Answered by | 29 Mar, 2017, 06:01: PM