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If AB is a chord of a circle with centre O, AOC is diameter and AT is the tangent at the point A.

Prove that ∠BAT=∠ACB

Asked by Nitesh Kansara(student) , on 18/1/13


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EXPERT ANSWER

Let ∠ACB = x and ∠BAT = y.

A tangent makes an angle of 90 degrees with the radius of a circle,

so we know that OAB + y = 900 ……..(1)
The angle in a semi-circle is 90, so CBA = 900 .
CBA + OAB + ∠ACB = 18 0 0   (Angle sum property of a triangle)
Therefore, 90 + OAB + x = 1800

So, OAB + x = 9 0 0………….(2)
But OAB + y = 900

Therefore, OAB + y = OAB + x  ………….[From (1) and (2)]
x = y.

Hence ∠ACB = ∠BAT.

 

Posted by Tushar Kohli(MeritNation Expert)on 22/1/13

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