Question

Ab and cd are two chords of a circle subtending 60 and 120 respectively at same point of circumference of circle.Then ab:cd

Answer 1

Answer: ab:cd= 1:2

Step-by-step explanation:

The angle subtended by the chords are proportional to length of the chords respectively.

So,

ab:cd= 60:120

=> ab:cd= 1:2

Answer 2

Answer:

AB : CD = 1 : 1

Step-by-step explanation:

∠AXB = 60°

⇒ ∠AOB = 120° ( because the angle which is subtended by an arc at the centre of a circle is double the size of the angle subtended at any point on the circumference).

and ∠AOB = ∠COD = 120° ( Vertically opposite angles )

Now, In ΔCOD and ΔBOA

CO = BO ( radius of same circle )

∠COD = ∠BOA ( Vertically opposite angles )

OD = OA ( radius of same circle )

So, By SAS postulate of congruency of triangles , ΔCOD ≅ ΔBOA

Therefore, CD = AB . So, AB : CD = 1 : 1