Question

3) In the figure, seg AB is a diameter
of the circle with centre 0. The
bisector of the inscribed < ACB
intersects the circle in point D.
Then prove that seg OD perpendicular seg AB
​

Answer 1

Draw seg OD.

⇒ ∠ACB=90

o

[ Angle inscribed in semicircle ]

⇒ ∠ACB=45

o

[ CD is the bisector of ∠C ]

⇒ m(arcDB)=2∠ACB=90

o

[ Inscribed angle theorem ]

⇒ ∠DOB=90

o

[ Definition measure of an arc ] ----- ( 1 )

⇒ segOA≅segOB [ Radii of the circle ] ----- ( 2 )

∴ Line OD is perpendicular bisector of segAB [ From ( 1 ) and ( 2 ) ]

∴ segAD≅segBD

solution