MathDB

A4

Part of 2018 Malaysia National Olympiad

Problems(3)

OMK 2018 Sulong, Section A Problem 4

Source: OMK 2018 Sulong, Section A Problem 4

6/21/2021
Given a circle with diameter ABAB. Points CC and DD are selected on the circumference of the circle such that the chord CDCD intersects ABAB inside the circle, at point PP. The ratio of the arc length \overarc {AC} to the arc length \overarc {BD} is 4:14 : 1 , while the ratio of the arc length \overarc{AD} to the arc length \overarc {BC} is 3:23 : 2 . Find ∠APC\angle{APC} , in degrees.
geometrycontests
sum of a areas, parts of regular octagon 2018 Malaysia OMK Intermediate A4

Source:

9/19/2021
Given a regular octagon ABCDEFGHABCDEFGH with side length 33. By drawing the four diagonals AFAF, BEBE, CHCH, and DGDG, the octagon is divided into a square, four triangles, and four rectangles. Find the sum of the areas of the square and the four triangles.
geometryoctagonareas
max distance among collinear points 2018 Malaysia OMK Juniors A4

Source:

9/19/2021
Given points A,B,C,D,EA, B, C, D, E, and FF on a line (not necessarily in that order) with AB=2AB = 2, BC=6BC = 6, CD=8CD = 8, DE=10DE = 10, EF=20EF = 20, and FA=22FA = 22. Find the distance between the two furthest points on the line.
algebra