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Question 4
If AB is a chord of a circle with centre O, AOC is a diameter and tangent T at A as shown in the figure. Prove that BAT = ACB.


 


Solution

AC is a diameter.
We know that angle in a semi-circle is 90.
ABC=90             [ by property]
In Δ ABC.    CAB+ABC+ACB=180
[ sum of all interior angles of any triangle is 180]
CAB+ACB=18090=90 ...(i)
Since , diameter of a circle is perpendicular to the tangent.
i.e        CA  AT
CAT=90
CAB+BAT=90 ...(ii)
From Eqs. (i) and (ii)    
CAB+ACB=CAB+BAT
ACB=BAT       
Hence proved.

Mathematics
NCERT Exemplar
Standard X

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