Let 4ABC be inscribed in a circle with center O with AB = 13, BC = 14, AC = 15. Let the foot of the perpendicular from A to BC be D and let AO intersect BC at E. Given the length of DE can be
expressed as m
n
where m, n are relatively prime positive integers, find m + n.

The avenues in a particular city run north to south and are numbered consecutively with 1st avenue at the western border of the city. the streets in the city run east to west and are numbered consecutively with 1st street at the southern border of the city. for a festival, the city is not allowing cars to park in a rectangular region bordered by 5th avenue to the west. 9th avenue to the east, 4th street to the south, and 6th street to the north. if x is the avenue number and yis the street number, which of the following systems describes the region in which cars are not allowed to park? 5th ave 9th ave

This is about circle theorems. someone asap : (

Due to bad planning, two of the local schools have their annual plays on the same weekend. while 457 people attend one, and 372 attend the other, only 104 people were able to attend both. how many people went to at least one play?