Bunuel wrote:
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?
A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3
Useful property:
a convex quadrilateral can be inscribed in a circle if and only its opposite angles are supplementary (supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°).
We can see on the diagram that only I and III meet that requirements.
Answer: C.
Hope it's clear.
I agree with "the opposite angles are supplementary" concept and I did the same.
Can this be a solution @Bunuel ?
1. for first diagram - Moreover, isn't the first one isoceles trapezium ? Isn't that sufficient ?
2. for third diagram - Parallelogram inscribed in a circle will become a rectangle (think of shape shifting)