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.

A triangle ABC is inscribed in a circle. If sum of the squares of sides of the triangle is equal to twice the square of the diameter then sin^2A+sin^2B+sin^2C is equal to

Angles opposite to two equal sides of a triangle are equal.

The area of a triangle is half the product of any of its sides and the corresponding altitude.

a and b are two side adjacent to the right angle of a right-angled triangle and p is the perpendicular drawn to the hypotenuse from the opposite vertex. Then p^(2) is equal to

The area of a triangle is 615 m^(2) . If one of its sides is 123 metre, find the length of the perpendicular dropped on that side from opposite vertex.

A triangle of maximum area is inscribed in a circle.If a side of the triangle is 20sqrt(3) then the radius of the circle is

Which of the following statements are true (T) and which are false (F)? Sum of the three sides of a triangle is less than the sum of its three altitudes. Sum of any two sides of a triangle is greater than twice the median drawn to the third side. Sum of any two sides of a triangle is greater than the third side. Difference of any two sides of a triangle is equal to the third side. If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. 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.