Mathematics
Three circles of radii 2 cm, 3 cm and 4 cm touch each other externally. Find the perimeter of the triangle obtained on joining the centres of these circles.
Answer
Three circles with centres A, B and C touch each other externally and the radii of these circles are 2 cm, 3 cm and 4 cm respectively.
From figure,
By joining the centres of circles, triangle ABC is formed in which,
AB = 2 + 3 = 5 cm
BC = 3 + 4 = 7 cm
CA = 4 + 2 = 6 cm.
Therefore, perimeter of the triangle ABC = AB + BC + CA = 5 + 7 + 6 = 18 cm.
Hence, the perimeter of triangle ABC = 18 cm.
Related Questions
In the figure (ii) given below, ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with vertices A, B and C as their centres. Find the radii of the three circles.
In the given figure, PB is a tangent to a circle with centre O at B. AB is a chord of length 24 cm at a distance of 5 cm from the centre. If the length of the tangent is 20 cm, find the length of OP.
In the figure (i) given below, the sides of the quadrilateral touch the circle. Prove that AB + CD = BC + DA.
