In Δ ABC, the perpendicular from vertices A and B on their opposite sides meet (when produced) the circumcircle of the triangle at points D and E respectively. Prove that: arc CD = arc CE
Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.
Two circle with centres A and B, and radii 5 cm and 3 cm, touch each other internally. If the perpendicular bisector of the segment AB meets the bigger circle in P and Q; find the length of
In the given figure, AC is a diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, q and r in terms of x .
In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centres of
the circles. Show that:
(i) AB = CD,
(ii) AC = BD.
In the given figure, M is the centre of the circle. Chords AB and CD are perpendicular to each other.
If ∠MAD = x and ∠BAC = y:
(i) express ∠AMD in terms of x.
(ii) express ∠ABD in terms of y.
(iii) prove that: x = y.