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Q.

Is the following statement true or false?


From an external point, if two tangents are drawn to a circle then they subtend equal angles at the centre.


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a

True

b

False 

answer is A.

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Detailed Solution

Given a statement, from an external point, if two tangents are drawn to a circle then they subtend equal angles at the centre.
If triangles are similar then all three sides in one triangle are in the same proportion to the corresponding sides in the other; it is called the SSS similarity criterion.
Question ImageAccording to the question,
PT  and  PQ   are drawn to a circle from an external point P  .
Computing that ∠POT = ∠QOT  ,
Considering ΔOPT  and ΔOQT  ,
OP=OQ  
OT=OT   (Common side)
PT = PQ   [ tangents drawn from same external point]
BY SSS   criterion we get,
ΔOPT≅ΔOQT   ∠POT = ∠QOT  [The corresponding parts of congruent triangles are congruent]
Therefore PT  and PQ   subtend equal angles at the center which is true.
Thus the correct option is 1.
 
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Is the following statement true or false?From an external point, if two tangents are drawn to a circle then they subtend equal angles at the centre.