Q. 115.0( 1 Vote )

# If two chords AB and CD of a circle with centre O, when produced intersect each other at the point P, let us prove that ∠AOC - ∠BOD = 2 ∠BPC.

Answer :

The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

Similarly, the angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

⇒ ∠BOD = 2∠BCD.

In ΔBPC, ∠ABC = ∠BPC + ∠BCP

On substituting the values of ∠ABC and ∠BCP in above

equation, we get,

⇒ ∠AOC - ∠BOD = 2 ∠BPC

Hence, proved.

Rate this question :

If two chords AB and CD of a circle with centre O, when produced intersect each other at the point P, let us prove that ∠AOC - ∠BOD = 2 ∠BPC.

West Bengal Board - MathematicsTwo chords AB and CD of a circle with centre O intersect each other at the points P, let us prove that ∠AOD + ∠BOC = 2∠BPC.

If AOD and BOC are supplementary to each other, let us prove that the two chords are perpendicular to each other.

West Bengal Board - MathematicsIn the adjoining figure, if O is the centre of circle, the then the value of x is

West Bengal Board - MathematicsWe drew a circle with the point A of quadrilateral ABCD as centre which passes through the points B,C and D. Let us prove that ∠CBD + ∠ CDB =

West Bengal Board - MathematicsIn the adjacent figure O is the centre of the circle; ∠AOD = 40° and ∠ACB = 35°; let us write by calculating the value of ∠BCO and ∠BOD, and answer with reason.

West Bengal Board - Mathematics

In the adjoining figure, if ‘O’ is the centre of circle and PQ is a diameter, then the value of x is

West Bengal Board - Mathematics

In the adjoining figure, if O is centre of circle, the value of ∠POR is

West Bengal Board - Mathematics