Prove that if two circles are drawn with two smaller sides of sacalene triangle as their diameter, then the points of c intersection of the two circles lie in the third side.

Prove that the circle drawn with any one of the equal sides of an isosceles triangle as diameter bisects the unequal side.

If two intersecting chords of a circle make equal angles with diameter passing through their point of intersection, prove that the chords are equal.

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

Prove that if equilateral triangles are drawn on the sides of a right-angled triangles then the area of the equilateral triangle, drawn on the hypotenuse is equal to the sum of the areas of the other two equilateral triangals drawn on its other two sides.

Prove that if two tangents are drawn to a circle from a point outside it, then the line segments joining the point of contacts and the exterior point are equal.

Find the locus of the circumcenter of a triangle whose two sides are along the coordinate axes and the third side passes through the point of intersection of the line a x+b y+c=0 and l x+m y+n=0.

Each of the two equal circles passes through the centre of the other and the two circles intersect each other at the points. A and B.If a straight ine through the point A intersects the two circles at points C and D prove that Delta BCD is an equilateral triangle.

Prove by the theorem of Thales that the third side of a triangle is parallel to the line segment obtained by joining the mid-points of any two sides of the triangle and is half in length of its third side.

If the area of the square drawn on any side of a triangle is equal to the sum of the areas of the squares drawn on the other two sides of the triangle ,then the triangle will be right-angled triangle, the opposite angle of the greatest side of which will be "......................" .