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Explore the Back-StoryTry this beautiful problem from the PRMO, 2019 based on Lines and Angles.

On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+ where a b c are positive integers with and in the reduced form. find a+b+c.

- is 107
- is 51
- is 840
- cannot be determined from the given information

Lines

Algebra

Angles

Answer: is 51.

PRMO, 2019, Question 7

Higher Algebra by Hall and Knight

Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min

x min after 12 is 6x -=90 or 270 (in degrees) then x =16 or 49

Difference 32 then a+b+c=32+8+11=51.

- https://www.cheenta.com/smallest-perimeter-of-triangle-aime-2015-question-11/
- https://www.youtube.com/watch?v=ST58GTF95t4&t=140s

Try this beautiful problem from the PRMO, 2019 based on Lines and Angles.

On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+ where a b c are positive integers with and in the reduced form. find a+b+c.

- is 107
- is 51
- is 840
- cannot be determined from the given information

Lines

Algebra

Angles

Answer: is 51.

PRMO, 2019, Question 7

Higher Algebra by Hall and Knight

Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min

x min after 12 is 6x -=90 or 270 (in degrees) then x =16 or 49

Difference 32 then a+b+c=32+8+11=51.

- https://www.cheenta.com/smallest-perimeter-of-triangle-aime-2015-question-11/
- https://www.youtube.com/watch?v=ST58GTF95t4&t=140s

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