If one vertex of the triangle having maximum area that can be inscribed in the circle `|z-i|=5` is `3-3i`, then find the other vertices of the triangle.

In the figure, a side of the triangle is 12 centimetres and the angle at its ends are are 45∘ and 60∘ i) Find the length of the other two sides of the triangle. ii) Find the perimeter of this triangle.

Let x and y be the length and bredth of the rectangle ABCD in a circle having radius r. Let angleCAB=theta (Ref. Figure). If triangle represent area of the rectangle and r is a constant. Show that the rectangle of maximum area that can be inscribed in a circle of radius r is a square of side sqrt2r .

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

Draw a circle and a triangle with one vertex at the center of the circle and the other two on the circle. Draw another triangle of the same area with all three vertices on the circle.

Consider a triangle whose sides are y = x, y = 2x and y = 3x + 4 Find the co-ordinates of the vertices of the triangle.

Consider a triangle whose sides are along x+y = 2, 3x-4y = 6 and x-y = 0 Find the vertices of the triangle

Rectangles are inscribed inside a semi-circle of radius r. Find the rectangle with maximum area.