Q14 of 22 Page 126

Let us write whether the following statements are true of false”

(i) In the adjoining figure, if O is centre of circle, then ∠AOB = 2 ∠ACD



(ii) The point O lies within the triangular region ABC in such a way that OA = OB and ∠AOB = 2∠ACB. If we draw a circle with centre O and length of radius OA, then the point c lies on the circle.

(i) False


For the given condition to happen, the angles should be subtended by the same arc only.


(ii) True


The given statement is true, due to the following theorem:-


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. Therefore, point C lies on circle.


More from this chapter

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14

O is the circumcentre of Δ ABC and ∠OAB = 50°, then the value of ∠ACB is

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

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Let us fill in the blanks

(i) The angle at the centre is ______ the angle on the circle, subtended by the same arc.


(ii) The length of two chord AB and CD are equal of a circle with centre O. If ∠APB and ∠DQC are angles on the circle, then the values of the two angles are_______.


(iii) If O is the circumcentre of equilateral triangle, then the value of the front angle formed by any side of the triangle is_______.

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In the adjoining figure, O is the centre of the circle, if ∠ACB = 30°, ∠ABC = 60°, ∠DAB = 35° and ∠DBC = x°, the value of x is