Prove that the tangent and the radius through the point of contact of a circle are perpendicular to each other.

The tangent to a circle and the radius passing through the point of contact are perpendicular to each other.

prove that the diagonals of a rhombus are perpendicular to each other.

Prove that the tangent to the circle at any point on it is perpendicular to the radius passes through the point of contact.

Show that , The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line - segment joining the points of contact at the centre.

XY is a diameter of a circle. PAQ is a tangent to the circle at the point A lying on the circumference. The perpendicular drawn on the tangent to the circle from X intersects PAQ at Z. Prove that XA is a bisector of angle YXZ." "[GP-X]

Two chords AB and CD of a circle with centre O intersect each other at the point P. prove that AOD+ angle BOC = 2 angle PBC . If angle BOC are supplementary to each other, then prove that the two chords are perpendicular to each other.

Tangent drawn from the point (a ,3) to the circle 2x^2+2y^2=25 will be perpendicular to each other if a equals (a) 5 (b) -4 (c) 4 (d) -5

Two circles intersect each other at the points G and H . A straight line is drawn through the point G which intersect two circles at the points P and Q and the straight line through the point H parallel to PQ intersects the two circles at the points R and S . Prove that PQ=RS .

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.