Question

If arcs AXB and CYD of a circle are congruent,find the ratio of chord AB and chord CD

Answer 1

◆Ekansh Nimbalkar◆
hello friend here is your required answer
Sol.We have AXB=~CYD
since if two arcs of a circle are congruent,then their corresponding arcs are equal,so we have chord AB=chord CD
Hence. AB:CD=1:1

Answer 2

The ratio of chord AB and chord CD is 1 : 1

Step-by-step explanation:

Let us find the ratio of chord AB and chord CD.

Given data:

arc AXB ≅ arc CYD

⇒ arc AXB = arc CYD

We know that chords corresponding to equal arcs are equal in length.

⇒ Chord AB = chord CD

⇒ AB = CD

Divide by CD on both sides of the equation.

$\Rightarrow \frac{AB}{CD} =\frac{CD}{CD}$

$\Rightarrow \frac{AB}{CD} =\frac{1}{1}$

⇒ AB : CD = 1 : 1

Hence the ratio of chord AB and chord CD is 1 : 1.

To learn more...

1. Given : chord AB = chord BC =  chord AC, ZBAP = ZCAP.

To prove: Seg CB = seg CQ.​

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2. Given chord AB = chord BC=  chord AC,<BAP -< CAP

To prove: Seg CB=seg Co.​

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