Assertion (A): The point which is equidistant from three non-collinear points D, E and F is the circumcentre of ΔDEF.
Reason (R): The incentre of a triangle is the point where the bisectors of the angles intersect.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
The circumcentre of a triangle is equidistant from its three vertices. So, the point which is equidistant from the three non-collinear points D, E and F is the circumcentre of ΔDEF.
∴ Assertion (A) is true.
The incentre of a triangle is the point of intersection of its angle bisectors.
∴ Reason (R) is true.
Reason (R) states a property of the incentre, which is unrelated to the property of the circumcentre stated in the Assertion. So, R is not the correct explanation of A.
Hence, option 2 is the correct option.