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  • Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

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Solution
According to question
         

To Prove :\angle Q_{1}= \angle Q_{2}
  X1, Y1, X2, Y2 are tangents at point A and B respectively.

Take a point C and join AC and AB.
Now \angle Q_{1}= \angle C          …..(i)   (Angle in alternate segment)
Similarly,
\angle Q_{2}= \angle C      …..(ii)
From equation (i) and (ii)
\angle Q_{1}= \angle Q_{2}= \angle C …..(iii)
From equation (3)
\angle Q_{1}= \angle Q_{2} 
Hence Proved

 

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