In Figure, circle `C(O ,r)a n dC(O^(prime)r/2)` touch internally at a point. `Aa n dA B` is a chord of the circle `C(O , r)` intersecting `C(O^(prime), r/2)` at `C` . Prove that `A C=C B`

In Figure,circle C(O,r) andC (O'(r)/(2)) touch internally at a point.Aand AB is a chord of the circle C(O,r) intersecting C(O',(r)/(2)) at C. Prove that AC=CB

Circles C(o, r) and C(O^(1), (r)/(2)) touch internally at a point A and AB is a chord of the circle intersecting C(O^(1), (r)/(2)) at C. Then AC is equal to :

Circles C(O, r) and C(O', r'), (r gt r') touch internally at P. PQ is a chord of circle C(O, r) which intersects C(O', r') at R. Show that OO'RQ is a trapezium

Circles C(O, r) and C(O', r'), (r gt r') touch internally at P. PQ is a chord of circle C(O, r) which intersects C(O', r') at R. Show that OO'RQ is a trapezium

Two equal chords AB and CD of a circle C(O,r) when produced meet at a point E. Prove that: BE = DE

In the given figure, two circles with centres O and O' touch externally at a point A. A line through A is drawn to intersect these circles at B and C. Prove that the tangents at B and C are parallel.

In Figure, O\ a n d\ O ' are centres of two circles intersecting at B\ a n d\ C. A C D is a straight line, find x .

In Figure, two tangents A Ba n dA C are drawn to a circle with centre O such that /_B A C=120^0dot Prove that O A=2A B

In a circle with centre O , chords A Ba n dC D intersect inside the circumference at Edot Prove that /_A O C+/_B O D=2/_A E Cdot

AOB is a diameter of a circle with centre O and C is any point on the circle, joining A, C, B, C, and O, C, prove that tanangleABC=cotangleACO