The P lies on side AB of an equilateral triangle ABC. Arrange AC, AP and CP in descending order.

The side AB of an equilateral triangle ABC is parallel to the x-axis. Find the slopes of all its sides.

Let a point P lies inside an equilateral triangle ABC such that its perpendicular distances from sides are P_(1),P_(2),P_(3) .If side length of triangle ABC is 2 unit then

On the sides AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn. Prove that : angleCAD=angleBAE

On the sides AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn. Prove that : (i) angle CAD = angle BAE (ii) CD = BE

Let the point P lies in the interior of an equilateral triangle with side lengths 2 units, each. Find the sum of the shortest distances from P to the sides of the triangle.

D is a point in side BC of triangle ABC. If AD gt AC , show that AB gt AC .

Sides AB and AC in an equilateral triangle ABC with side length 3 is extended to form two rays from point A as shown in the figure. Point P is chosen outside the triangle ABC and between the two rays such that angleABP+angleBCP=180^(@) . If the maximum length of CP is M, then M^(2)//2 is equal to :

The side of a triangle are in A.P. Its area is 3/5 the of an equilateral triangle of the same perimeter. Show that the sides are in the proportion 3:5:7 .

Construct an equilateral Delta ABC such that AB =4.2 cm.

The sides of a triangle are in A.P. and its area is 3/5t h of the an equilateral triangle of the same perimeter, prove that its sides are in the ratio 3:5:7, and find the greatest angle of the triangle.