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If AB is chord of a circle with centre O...

If AB is chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure. Prove that `angleBAT=angleACB.`

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Given : Chord AB, diameter AOC and tangent at A of a circle with centre O.
To Prove : `angleBAT=angleACB`
Proof : Radius OA and tangent AT at A are perpendicular.
`:." "angleOAT=90^(@)" "implies" "angleBAT=90^(@)-angle1" "...(2)`
AOC is a diameter.
`:." "angleB=90^(@)" "`(angle in a semicircle is right angle)
`implies" "angleC+angle1=90^(@)" "`(angle sum property)
`implies" "angleC=90^(@)-angle1" "...(2)`
From (1) and (2). we get `angleBAT=angleACB`
Hence Proved.
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