- #1
robobuggg
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Q1
Two circles intersect at P and Q. Two parallel line segments APC and BQD are drawn to meet one circle at A and C, and the other circle at B and D. PB and PD are diameters of their respective circles. Prove that points B, Q and D are collinear.
Q2
AB and CD are two parallel chords of a circle. If two other chords BF and DE are drawn such that they are parallel, prove that AE is parallel to CF.
For the first question, I'm not even sure how to draw it, as I don't see how A and C could be point on the same circle if the line goes through APC. I also don't understand why it's asking to prove BQD is collinear if it has already said that BQD is a (straight) line segment.
I've drawn a diagram for Q2, but I find that it's difficult to always know where to start with proofs. Any help would be much appreciated :)
Two circles intersect at P and Q. Two parallel line segments APC and BQD are drawn to meet one circle at A and C, and the other circle at B and D. PB and PD are diameters of their respective circles. Prove that points B, Q and D are collinear.
Q2
AB and CD are two parallel chords of a circle. If two other chords BF and DE are drawn such that they are parallel, prove that AE is parallel to CF.
For the first question, I'm not even sure how to draw it, as I don't see how A and C could be point on the same circle if the line goes through APC. I also don't understand why it's asking to prove BQD is collinear if it has already said that BQD is a (straight) line segment.
I've drawn a diagram for Q2, but I find that it's difficult to always know where to start with proofs. Any help would be much appreciated :)