Unformatted text preview: centroid divides each median in the ratio 2 : 1. Exercises: 1. Let R be the circumradius of 4 ABC . Then abc = 4( ABC ) R ). 2. Let ABCD be a cyclic quadrilateral. Prove that AC ( AB · BC + CD · AD ) = BD ( AD · AB + BC · CD ) = 4 R ( ABCD ), where R is the radius of the circumcircle of the quadrilateral ABCD . 3. In the ﬁgure, the cevians AD , BE , and CF of 4 ABC meet at P . Given that BD : DC = 5 : 4, AE : EC = 6 : 5, and ( APF ) = 48, ﬁnd ( BPF ). 4. Let M be the midpoint of the side AB of an equilateral triangle ABC . Let N be a point on BC such that MN ⊥ BC . Prove that 4 BN = BC . 5. In 4 ABC , a line m is drawn through its centroid G such that the vertices A and B are on the same side of m . Let X , Y , and Z be the feet of the perpendiculars of m from A , B , and C , respectively. Prove that AX + BY = CZ ....
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This note was uploaded on 11/15/2010 for the course MATH 100 taught by Professor B during the Spring '09 term at Ateneo de Manila University.
- Spring '09