Question : AB is the diameter of a circle having a centre at O. PQ is a chord that does not intersect AB. Join AP and BQ. If $\angle$BAP = $\angle$ABQ, then ABQP is a:

Option 1: cyclic square

Option 2: cyclic trapezium

Option 3: cyclic rhombus

Option 4: cyclic rectangle


Team Careers360 22nd Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: cyclic trapezium


Solution :
$\angle$BAP = $\angle$ABQ and AB $\neq$ PQ
Now, $\angle$BAP + $\angle$BQP = 180°
⇒ $\angle$ABQ + $\angle$BQP = 180°
⇒ AB || PQ
So, ABQP is a cyclic trapezium.
Hence, the correct answer is cyclic trapezium.

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