A straight line `AB` is divided at `C` so that `AC=3CB`. Circles are described on `AC and CB` as diameters and a common tangent meets `AB` produced at `D`. Show that `BD` is equal to the radius of the smaller circle.

AB is a diameter of a circle. CD is a chord parallel to AB and 2CD = AB . The tangent at B meets the line AC produced at E then AE is equal to -

In the given figure AB is the diameter and AC is the chord of a circle such that /_BAC=30^(@) . The tangent at C intersects AB produced at D. Prove that :BC=BD.

In figure, AB and CD are common tangents to two circles of equal radii. Prove that AB=CD.

AB is the diameter and AC is a chord of a circle with centre O such that angle BAC=30^(@) . The tangent to the circle at C intersects AB produced in D. Show that BC=BD.

AB is a line segment and M is its mid point. Three semi circles are drawn with AM, MB and AB as diameters on the same side of the line AB. A circle with radius r unit is drawn so that it touches all thethree semi- circles. Show that AB=6xxr

ABC is an isosceles trianlge with AB=AC. A circle through B touches side AC at its middle point D and intersects side AB in point P. Show that AB=4xxAP .

In the given figure, O is the centre of the circle ans AB is a tangent at B. If AB=15 cm and AC=7.5cm, calculate the radius of the circle.

In the given figure, angleABC= 90^(@) and BC is diameter of the given circle. Show that: AC xx AD= AB^(2)

In figure, AB is a chord of the circle and AOC is its diameter such that angleACB=50^(@) . If AT is the tangent to the circle at the point A, then angleBAT is equal to

In the given figure O is the centre of the circle and AB is a tangents at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of the circle.