Prove and write the perpendicular axis theorem.

Write the parellel and perpendicular axis theorem.

Prove that the perpendicular at the points of contact to the tangents to a circle passes through the centre.

State and prove theorem of perpendicular axes.

O is a point in the interior of ∆ABC . OD,OE and OF are the perpendicular drawn to the sides BC, CA and AB respectively. Prove that AF^2+BD^2+CE^2=AE^2+BF^2+CD^2 .

A and D are two points on the perpendicular bisector of BC lying on the same side of BC. Prove that /_ABD = /_ACD .

If BD is the perpendicular drawn from the vertex B of the right triangle ABC to the hypotenuse AC,prove that(i) BD^2=ADxxDC

If BD is the perpendicular drawn from the vertex B of the right triangle ABC to the hypotenuse AC,prove that(iii) BC^2=CDxxAC

If BD is the perpendicular drawn from the vertex B of the right triangle ABC to the hypotenuse AC,prove that(ii) AB^2=ADxxAC

Prove that the locus of the centres of all circles passing through two given points A, B is the perpendicular bisector of the line segment AB.