If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC, prove that the points B, C, M and N are concyclic.
Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.
On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that ∠BAC = ∠BDC
O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.
ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that ∠CBD + ∠CDB =1/2 ∠BAD
Which are the two main climatic factors responsible for soil formation?
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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.
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