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

650 views

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  posted May 1, 2016

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 May 1, 2016

All the given statements are true as it is an equilateral triangle. answer May 2, 2016

Similar Puzzles

Three non-concentric circles of equal radii are drawn such that each circle touches the other two externally. The centres are joined to form a triangle whose area is 17320.5 cm^2. Find the area of the triangle not included in the circles. Two circles are drawn inside a square with side length 2 + SQRT(2) as shown in the figure. Let the radius of the larger circle be R and the radius of the smaller circle be r . Find the value of R + r In the figure if AC is a common tangent of two touching circles. If B is the touching point of both circles then which is of the following is true about it and why...

1. Angle B is a right angle
2. Angle B is an obtuse angle
3. Angle B is an acute angle
4. There is not enough information to know anything about Angle B. +1 vote

In the figure AC is a common tangent of two touching circles. If B is touching point of both circles then find angle B. +1 vote

How many more triangles in the given figure must be shaded to make the fraction of unshaded part equal to 5/8? 