MathDB

4

Part of 2010 Malaysia National Olympiad

Problems(3)

angle wanted, equal ones, 68^o, 72^o- Malaysia 2010 OMK Bongsu / Juniors p4

Source:

10/26/2021
In the diagram, ∠AOB=∠BOC\angle AOB = \angle BOC and∠COD=∠DOE=∠EOF\angle COD = \angle DOE = \angle EOF. Given that ∠AOD=82o\angle AOD = 82^o and ∠BOE=68o\angle BOE = 68^o. Find ∠AOF\angle AOF. https://cdn.artofproblemsolving.com/attachments/b/2/deba6cd740adbf033ad884fff8e13cd21d9c5a.png
geometryangles
2 squares and 1 circle - Malaysia 2010 OMK Muda / Intermediate p4

Source:

10/26/2021
A square ABCDABCD has side length 1 1. A circle passes through the vertices of the square. Let P,Q,R,SP, Q, R, S be the midpoints of the arcs which are symmetrical to the arcs ABAB, BCBC, CDCD, DADA when reflected on sides ABAB, BBC, CDCD, DADA, respectively. The area of square PQRSPQRS is a+b2a+b\sqrt2, where aa and b b are integers. Find the value of a+ba+b. https://cdn.artofproblemsolving.com/attachments/4/3/fc9e1bd71b26cfd9ff076db7aa0a396ae64e72.png
geometry
OMK 2010

Source: Malaysia National Olympiad 2010 Sulung Category Problem 4

6/4/2011
A semicircle has diameter XYXY. A square PQRSPQRS with side length 12 is inscribed in the semicircle with PP and SS on the diameter. Square STUVSTUV has TT on RSRS, UU on the semicircle, and VV on XYXY. What is the area of STUVSTUV?
geometrygeometry unsolved