Answered: ABCD is a cyclic quadrilateral and AB…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let ABCD be a convex quadrilateral, and let M be the intersection of its diagonals AC and BD. Suppose the sides BA and CD, when extended, intersect, say at H. Then ABCD is cyclic if and only if any one of the following conditions holds: 1.
1. Given parallelogram ABCD, F is a point on BC, E is the intersection of DF and AB. Prove that FCD ~ FBE.
On the sides of a triangle ABC, squares ABDE, ACFG, BCJK are constructed externally to it. BF, AJ, CD, AK are joined. If FC, DB are produced to meet AJ, AK in H, I respectively and X, Y are the intersections of BF, CD with AC, AB respectively, show that X, H are equidistant from C and Y, I are also equidistant from B. Prove also that the perpendiculars from A, B, C on GE, DK, FJ respectively intersect in the centroid of the triangle ABC and that GE, DK, FJ are respectively double the medians from A, B, C. G F R M J K

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ABCD is a cyclic quadrilateral and AB and DC are produced to meet at Q, and BC and AD are produced to meet at R, prove that QP and RP, the bisectors of the angles BQC and CRD respectively, are at right angles to each other.