XY and X'Y' are two parallel tangents to the circle with centre at O. Antoher tangent AB touches the circle at C and XY at A and X'Y' at B. Prove that `angleAOB=90^(@)` .

Choose the correct answer and give justification for each. In the figure XY and X^(1)Y^(1) are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X^(1)Y^(1) at B then /_AOB=

AB and AC are two tangents to the circle with centre at O. Prove that AO bisects the chord passing through point of contact at right angle.

If y= 3x is a tangent to a circle with centre (1, 1) , then the other tangent drawn throught (0, 0) to the circle is-

Two tangents are drawn from an external point A of the circle with centre at O which touches the circle at the points B and C. Prove that AO is the perpendicular bisector of BC.

Two tangents are draw from an external point A to the cirle with centre at O. If they touch the circel at the point B and C then prove that AO is the perpendicular bisector of BC.

Two circles touch externally at P. A direct common tangent AB to two circles touch the circles at A and B. Then the measure of angleAPB is

OA and OB are the radius of a circle with centre at O and angleAOB= 150^@ . The tangents at A and B intersects at C. Find angleACB .

The tangent drawn from an extenral point A of the circle with centre C touches the circle at B. If BC =5 cm, AC=13 cm, then the length of AB=

AB is a diameter of a circle. BP is a tangent to the circle at B . A straight line passing through A intersects BP at C and the circle at D . Prove that BC^(2)=ACxxCD .