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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 r is the radius of S and R is the radius of S2, then which one of the following is correct?

  5. If m is the area of the circle S and n is the area of semi-circle S1, then which one of the following is correct?

  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. Two circles touch externally. The sum of their areas is 89π square cm and the distance between their centres is 13 cm. What is the difference in their radii?

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


Important Questions from Circles, Chords and Tangents

  1. A chord 21 cm long is drawn in a circle of diameter 25 cm. The perpendicular distance of the chord from the centre is:

  2. 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 ?

  3. In a circle with radius 5 cm, a chord is at a distance of 3 cm from the centre. The length of the chord is:

  4. 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?

  5. In a circle with centre O, an arc ABC subtends an angle of 132° at the center of the circle. Chord AB is produced to point P. Then ∠CBP is equal to∶

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