Q.

State whether true or false


In the figure, CD is a diameter of the circle with center O. Diameter CD is perpendicular to chord AB at point E. Then  ΔABCis an isosceles triangle.


E.png

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a

True

b

False 

answer is A.

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Detailed Solution

The statement is true.
Consider ΔACE   and ΔBCE  
In these triangles,
CE = CE  
AEC=BEC= 90  
AE = EB  
Therefore, ΔACEΔBCE   by SAS
Hence, by corresponding parts of congruent triangles: AC=BC
Since , two sides are equal ΔABC   is an isosceles triangle.
The statement is true.
 
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