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In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues uptofive times. What is the ratio of the area of fourth triangle to that of sixth triangle? (Original triangle is counted as 1st triangle)
ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ∠BPC?
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues up to seven times. What is the ratio of the area of fourth triangle to that of seventh triangle?
If the ratio of the angles of a triangle is 2 : 4 : 3, then what is the sum of the smallest angle of the triangle and the largest angle of the triangle? A. 120 degrees B. 100 degrees C. 140 degrees D. 110 degrees
Calculate the number of equilateral triangle that can be produced by melting and recasting a metallic sphere having a radius equal in length to the side of equilateral triangle.  (The equilateral triangle and sphere are having uniform thickness and also there is no loss of material in melting and recasting).
A circle of maximum area is inscribed in the square. An equilateral triangle is inscribed in that circle and all the vertices of the triangle touch the circle. A triangle is formed by the joining of the midpoint of the sides of the equilateral triangle. Find the ratio of the area of the square and area of the triangle which is formed by midpoints.
The side of an equilateral triangle ABC is 28 cm. Find the side of another equilateral PQR whose area is 16 times the area of triangle ABC.
ABC is an equilateral triangle of side 6 cm. If a circle of radius 1 cm is moving inside and along the sides of the triangle, then the locus of the centre of the circle is an equilateral triangle of side is
Which of the following statements is/are true? A: If in ΔABC, O is the orthocenter of the circle, then ∠BOC will be (90 + ∠BAC). B: Each side of an equilateral triangle is 2/√3 times of its height. C: If two transversal lines cuts two parallel lines ‘L’ at A and B and ‘M’ at C and D. If the two transversal lines cut each other at O somewhere between two parallel lines, then ΔAOB and ΔCOD will be similar.
Consider the following statements: I. If three equal circles are drawn on the vertex of equilateral triangle in such a way that all the circles touch each other externally then the triangle is equilateral triangle. II. The circum centre of any triangle cannot be lie on its side.