MathDB

7

Part of 2013 Online Math Open Problems

Problems(2)

2012-2013 Winter OMO #7

Source:

1/16/2013
Jacob's analog clock has 12 equally spaced tick marks on the perimeter, but all the digits have been erased, so he doesn't know which tick mark corresponds to which hour. Jacob takes an arbitrary tick mark and measures clockwise to the hour hand and minute hand. He measures that the minute hand is 300 degrees clockwise of the tick mark, and that the hour hand is 70 degrees clockwise of the same tick mark. If it is currently morning, how many minutes past midnight is it?
Ray Li
Online Math Opengeometryperimeter
2013-2014 Fall OMO #7

Source:

10/30/2013
Points MM, NN, PP are selected on sides AB‾\overline{AB}, AC‾\overline{AC}, BC‾\overline{BC}, respectively, of triangle ABCABC. Find the area of triangle MNPMNP given that AM=MB=BP=15AM=MB=BP=15 and AN=NC=CP=25AN=NC=CP=25.
Proposed by Evan Chen
Online Math Opengeometrytrigonometrysimilar triangles