top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

Three non-concentric circles of equal radii are drawn such that each circle touches the other two externally...

0 votes
362 views

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.

Area not included in triangles

posted Oct 30, 2015 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

1 Answer

0 votes

5236.6 sq cm. If the radius of each circle is a, the equilateral triangle has base 2a and height 1.73205 a giving the area equal to 1.732.5 a*a and equating this to 17320.5 gives a=100 cm. Since the angles of the triangle are 60 degrees, in each case the area of the triangle not included in the circle is 1/6th the area of the circle of 360 degrees. Each case this comes to one sixth of 3.142*100^2 that is 5236.6 sq cm

answer Mar 5, 2017 by Kewal Panesar



Similar Puzzles
+1 vote

Two congruent circles of radius 5 cm are drawn in such a way that one is 1 cm below the other . Find the area of red coloured region?

enter image description here

0 votes

I have 3 unit circles. Two of them are externally tangent to each other. The third one passes through the tangent point, cutting two symmetrical areas from those two circles, as shown in the diagram. What is the shaded area?

enter image description here

+3 votes

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

enter image description here

0 votes

A square contains a semicircle and a quarter circle, as shown. The two circles are tangent to each other. The semicircle has a diameter equal to 12 and the quarter circle has a radius equal to 12.
What is the area of the square?
What is the length of the tangent line segment AB?

enter image description here

0 votes

In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram.
What is the radius of the inscribed circle?

enter image description here

...