If a triangle is inscribed in a circle, then prove that the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the thrid side from the opposite vertex.

Show that the difference of any two sides of a triangle is less than the third side.

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.

An equilateral triangle is inscribed in a circle. If a side of the triangle is 12 cm. If a side of the triangle is 12 cm. Find the area of the circle.

Prove that any two sides of a triangle are together greater than twice the median drawn to the third side.

Which of the following statements are true (T) and which are false (F)? (i) Sum of the three sides of a triangle is less than the sum of its three altitudes. (ii) Sum of any two sides of a triangle is greater than twice the median drawn to the third side. (iii) Sum of any two sides of a triangle is greater than the third side. (iv) Difference of any two sides of a triangle is equal to the third side. (v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. (vi) Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.

An equilateral triangle is inscribed in a circle of radius 6cm. Find its side.

If circles are drawn taking two sides of a triangle as diameters, prove that the point ofintersection of these circles lie on the third side

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side

The line segment joining the mid-points of any two sides of a triangle in parallel to the third side and equal to half of it.

Prove that the line segment joining the mid points of two side of a triangle is parallel to the third side and equal to half of it.