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Question

An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. what is ∠BDC equal to?

This question was previously asked in
CDS II 2021 General Knowledge Previous Year Paper (14-Nov-2021)
The correct answer is

60°

The sum of opposite angles in a cyclic quadrilateral is 180^\circ . Angles in a semicircle are always 90^\circ . This is a special case of the angle subtended by an arc property, where the arc is a semicircle (180 degrees at the center). Hence, the correct answer is 60°.

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Similar Questions

  1. What is the length of QC ?

  2. What is the relation between x and y ?

  3. If y = 15, then what is ∠ACB equal to ?

  4. If ∠ABD = θ, then what is sin θ equal to ?  

  5. What is the radius of the circle ?

  6. What is the radius of the circle ?

  7. What is the area of the minor segment ?

  8. What is the area of the major segment ?
  9. What is the length of the chord a unit circle which subtends an angle 2θ at the centre, where θ < 45°?

  10. Consider the following statements :

    1. If two chords AB and AC of a circle are equal, then the centre of the circle lies on the angle bisector of angle CAB.

    2. If two concentric circles are intersected by a line at A, B, C and D respectively, then AC = BD.

    Which of the above statements is/are correct?


Important Questions from Circles, Chords and Tangents

  1. AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 112°, then what is the measure of ∠OAB ?

  2. The distance between the centres of two circles is 24 cm. If the radius of the two circles are 4 cm and 8 cm, then what is the sum of the lengths (in cm) of the direct common tangent and the transverse common tangent?

  3. What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?

  4. There are two identical circles of radius 10 cm each. If the length of the direct common tangent is 26 cm, then what is the length (in cm) of the transverse common tangent?

  5. AB is a chord in the minor segment of a circle with centre O. C is a point on the minor arc (between A and B). The tangents to the circle at A and B meet at a point P. If ∠ACB = 108°, then ∠APB is equal to:

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