Question

1 . Prove that equal chords of a circle subtend equal angle at the centre.
2. Prove that if chords of congruent circles subtend equal angles at their centers, then the chords
are equal.

PLS WRITE AND SEND GUYS

Answer 1

• In ΔAOB and ΔCOD,

AB=CD (Given)

AO=CO (radius)

OB=OD (radius)

By S.S.S congruency, ΔAOB≅ΔCOD

⇒∠AOB=∠COD.

_______&________________________

In △AOB and △PXQ

In △AOB and △PXQAO=PX [Radius of congruent circles are equal]

In △AOB and △PXQAO=PX [Radius of congruent circles are equal]∠AOB=∠PXQ [Given]

In △AOB and △PXQAO=PX [Radius of congruent circles are equal]∠AOB=∠PXQ [Given]BO=QX [Radius of congruent circles are equal]

In △AOB and △PXQAO=PX [Radius of congruent circles are equal]∠AOB=∠PXQ [Given]BO=QX [Radius of congruent circles are equal]△AOB≅△PXQ [SAS congruence rule]

In △AOB and △PXQAO=PX [Radius of congruent circles are equal]∠AOB=∠PXQ [Given]BO=QX [Radius of congruent circles are equal]△AOB≅△PXQ [SAS congruence rule]∴AB=PQ [CPCT]

NOTE

• IMAGE 1 FOR ANSWER 1

• IMAGE 2 FOR ANSWER 2