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Two intersecting circles C1 and C2 have a common tangent which touches C1 at S and C2 at T. The two circles intersect at X and Y, where Y is nearer to ST than X is.

Determine (with proof) the ratio:
Area(Triangle XYS)/Area(Triangle XYT)

(No Solution Yet, 1 Comments) Submitted on 2015-08-01 by K Sengupta   
Difficulty: 2 of 5 Bonus: What's the time, Mr Caesar? (in Numbers) Rating: 2.33
I own a very unique clock. It is digital, but it displays the time in Roman numerals. It does this in the same way as a normal digital clock (hours : minutes). The clock does not display seconds. For example, at 7:34 the clock displays "VII:XXXIV". Whenever a zero is required it is represented by a dash (-). That is, 1:00 is represented by "I:-".

Sometimes I place this clock on a flat, horizontal mirror which reflects what is displayed on the clock.

For what proportion of the day does the reflection of the time on the clock look the same as the time displayed by the clock itself?

Please provide an answer for both 12hr timing (the clock does not indicate the difference between AM and PM) and 24hr timing.

(Solution Posted, 5 Comments) Submitted on 2004-05-16 by Popstar Dave   
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