Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

What is the distance between two parallel tangents to a circle of radius 5cm?

What is the distance between two parallel tangents of a circle of radius 4cm?

The angle between two tangents to a circle may be 0^(@) .

Find the distance between two parallel tangents of a circle of radius 3 cm.

Prove that equal chords of a circle subtend equal angles at the centre.

Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.

Prove that the portion of the tangent to an ellipse intercepted between the ellipse and the directrix subtends a right angle at the corresponding focus.

The tangent at the point alpha on a standard ellipse meets the auxiliary circle in two points which subtends a right angle at the centre. Show that the eccentricity of the ellipse is (1+ sin^2aplha)^-1/2 .

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .