MathDB

3.3

Part of 2011 Saudi Arabia Pre-TST

Problems(2)

angles wanted in isosceles AB, BB'+ B'A = BC

Source: 2011 Saudi Arabia Pre-TST November 3.3

12/31/2021
In the isosceles triangle ABCABC, with AB=ACAB = AC, the angle bisector of ∠B\angle B intersects side ACAC at B′B'. Suppose that BB′+B′A=BC B B' + B'A = BC. Find the angles of the triangle.
geometryanglesisosceles
AP x BP x CP >= 8PL x PM x PN

Source: 2011 Saudi Arabia Pre-TST February 3.3 https://artofproblemsolving.com/community/c2745403_2011_

1/1/2022
Let PP be a point in the interior of triangle ABCABC. Lines APAP, BPBP, CPCP intersect sides BCBC, CACA, ABAB at LL, MM, NN, respec­tively. Prove that AP⋅BP⋅CP≥8PL⋅PM⋅PN.AP \cdot BP \cdot CP \ge 8PL \cdot PM \cdot PN.
geometrygeometric inequality