In the figure, seg AB is a diamete of the circle with centre 0. The bisector of the inscribed < ACB intersects the circle in point D.
Then prove that seg OD I seg AB
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In the figure, seg AB is a diamete of the circle with centre 0. The bisector of the inscribed < ACB intersects the circle in point D.
Then prove that seg OD I seg AB
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Answer: Step-by-step explanation:
Proof: Draw seg OD.
∠ACB=90° angle inscribed in semicircle
∠ACB=45° CD is the bisector of ∠C
m (arc DB) =2∠ACB=90° inscribed angle theorem
∠DOB=90° definition of measure of an arc
seg OA seg OB Radii of the circle
∴ line OD is prependicular bisector of seg AB.
∴ seg AD seg BD