KnowledgeBoat Logo
|

Mathematics

AB and CD are the chords of a circle with centre O, ∠AOB = 60° and angles ∠COD = 45°; the ratio between the length of the chords AB and CD is

AB and CD are the chords of a circle with centre O, ∠AOB = 60° and angles ∠COD = 45°; the ratio between the length of the chords AB and CD is: Circle, Concise Mathematics Solutions ICSE Class 9.

  1. 3 : 4

  2. 4 : 3

  3. 7 : 4

  4. 7 : 3

Circles

2 Likes

Answer

We know that,

Ratio of the angles subtended by the chords on the center is equal to the ratio of the length of the chords.

∴∠AOB∠COD=ABCD⇒60°45°=ABCD⇒43=ABCD\therefore \dfrac{\text{∠AOB}}{\text{∠COD}} = \dfrac{\text{AB}}{\text{CD}} \\[1em] \Rightarrow \dfrac{60°}{45°} = \dfrac{\text{AB}}{\text{CD}} \\[1em] \Rightarrow \dfrac{4}{3} = \dfrac{\text{AB}}{\text{CD}}

So, ratio between the length of the chords AB and CD is 4 : 3.

Hence, option 2 is the correct option.

Answered By

1 Like

Related Questions