If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.
AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.
A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent.
If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ≅ Arc PYB.
Write True or False and justify your answer.
If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A,
B, C, D are concyclic
Write True or False and justify your answer.
If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is
the centre of the circle through A, B and C.
Write True or False and justify your answer.
ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°
Write True or False and justify your answer.
A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.
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