Suppose wedraw a circlewith the bottom side of the triangles in the picture as diameter. Find out whether the top corner of each triangle is inside the circle, on the circle or outside the circle.

The bottom side of the quadrilateral in the picture is a diameter of the circle and the top side is ạ chord parallel to it. Calculate the area of the quadrilateral.

A circleis drawn with origin as the centre and radius 10 units.Show that the point (-8,-6) is a point on the circle. Find out whether the point (9,-1) lies within the circle or outside thecircle. Why?

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.

Prove that the.circumcentre of an equilateral triangle is the same as its centroid. i) Calculate the length of a side. of an equilateral triangle with vertices on a circle of diameter 1 ceritimetre. ii). Calculate the perimeter of such a triạngle.

Prove that the two circles drawn on the two equal sides of an isosceles triangle as diameters pass through the mid point of the third side.

In the picture below, two lines are drawn from the top vertex of a triangle to the bottom side: Prove that the ratio in which these lines divide the length of the bottom side is equal to the ratio of the area of the three smaller triangles in the picture.

Corners of a square are. on a circle. If the length of one side of square is 10 cm, find the perimeter of the circle.

The picture shows two circles with the same centre and two triangles formed by joining the centre to the points of intersection of the circles with two radii of the larger circle. prove that these triangles are similar .

Circle with centre O touches the sides of the triangle at P, Q and R, AB=AC , AQ=4 centimetres and CQ=6 centimetres.Find the perimeter and the area of the triangle. .