Question

In the following figure, what can be concluded from the given conditions.

Given: AB = CD and AC = DE.

• A. AC = BD,
• B. $\angle$AOC = $\angle$BOD.
• C. $\angle$AOB = $\angle$COD
• D. All of the above.

Answer 1

The correct option is D

All of the above.

Given that chords AB and CD are equal.

Therefore, the angles subtended by them at the centre are also equal.

$\angle$AOB = $\angle$COD

We can write $\angle$AOB = $\angle$AOC + $\angle$COB _________1

Similarly we can write $\angle$COD = $\angle$COB + $\angle$BOD ________2

From (1) and (2)

$\angle$AOB = $\angle$COD

$\angle$AOC + $\angle$COB = $\angle$COB + $\angle$BOD

Therefore, $\angle$AOC = $\angle$BOD

Therefore using converse of theorem, we get AC = BD.

Hence all the three given options are correct.