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ND
Guest
When you're proving something to be a cyclic quad, say ABCD, and you know that ACB=ADB, is the statement you make still "angles subtended in same segment are equal"?
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N
ND
Guest
Ok thanks, i might try putting "converse of" in front too.
underthesun
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Probably "chords subtend equal angles on a circle, hence ABCD is cyclic quad"?
a bit too long it seems...
a bit too long it seems...
The formal reason:
If the endpoints of an interval AB subtend equal angles at two points C and D on the same side of the interval, then the endpoints of the interval and the two points are concyclic.
Thus A, B, C, D lie on a circle, so ABCD is a cyclic quadrilateral.
(Note: That's the formal reason. You may be able to get away with writing less in the HSC)
If the endpoints of an interval AB subtend equal angles at two points C and D on the same side of the interval, then the endpoints of the interval and the two points are concyclic.
Thus A, B, C, D lie on a circle, so ABCD is a cyclic quadrilateral.
(Note: That's the formal reason. You may be able to get away with writing less in the HSC)