In the given figure, chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD

Open in App

Solution

chord AB ≅ chord CD (Given)

⇒ arc ACB ≅ arc CBD (Corresponding arcs of congruent chords of a circle are congruent)

⇒ m(arc ACB) = m(arc CBD)

⇒ m(arc AC) + m(arc CB) = m(arc CB) + m(arc BD)

⇒ m(arc AC) = m(arc BD)

⇒ arc AC ≅ arc BD (Two arcs are congruent if their measures are equal)

Suggest Corrections

Similar questions

A B ≅ c h o r d C D

a r c A C ≅ a r c B D

In the given figure, O is the centre of the circle. Chord AB is parallel to chord CD and CB is a diameter. Prove that arc AC = arc BD. [4 MARKS]

85^{\circ}

(3 k + 55)^{\circ}

k

A B

C D

A Y D Z B W C X

a r c (C X A) + a r c (D Z B) = a r c (A Y D) + a r c (B W C) = a r c (semicircle)

Join BYJU'S Learning Program