Three circles of equal radii all intersect at a single point as shown in figure, which of the following must be true?

Question

Three circles of equal radii all intersect at a single point P. Let the other intersections be A, B and C. Which of the following must be true?

a) P is the incentre of Triangle ABC
b) P is the circumcentre of Triangle ABC
c) P is the centroid of Triangle ABC
d) P is the orthocenter of Triangle ABC

Answer 1

In the figure, three circles of equal radia intersect at a single point P and other intersections are A, B, & C which formed equilateral triangle ABC.
In a equilateral triangle the incentre, Circumcentre , Centroid and Orthocentre coincide.
So a, b, c & d are all true.

Answer 2

All the given statements are true as it is an equilateral triangle.