If a triangle is inscribed in an ellipse and two of its sides are parallel to the given straight lines, then prove that the third side touches the fixed ellipse.

A triangle is inscribed in the hyperbola xy=c^2 and two of its sides are parallel to y=m_1 x and y = m_2 x . Prove that the third side touches the hyperbola 4m_1 m_2 xy = c^2 (m_1 + m_2)^2 .

Find the length of the third side of the triangle.

Find the length of the third side of the triangle.

An equilateral triangle is inscribed in an ellipse whose equation is x^2+4y^2=4 If one vertex of the triangle is (0,1) then the length of each side is

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

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

If two sides of a triangle are hati+2hatj and hati+hatk , then find the length of the third side.

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.

An equilateral triangle is inscribed in the parabola y^(2) = 8x with one of its vertices is the vertex of the parabola. Then, the length or the side or that triangle is

Theorem 6.2 : If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.