In triangle ABC, points D,E,F are on sides BC,CA,AB respectively such that AD,BE,CF are angle bisectors of triangle ABC. The linesAD,BE,CF are concurrent at I,the incenter of triangle ABC. If Angle BAC=90, what is the measure (in degrees) of Angle EIF?
f(x) is a cubic polynomial such that f(n)=1/n^2+1 for n=1,2,3,4. If f(0)=a/b,where a and b are coprime positive integers, what is the value of a+b
A rectangular prism has a volume of 250 cubic cm.What would the volume be if one dimension stayed the same, a second dimension was three times as long, and the third was twice as long?
Andrew has ten different two-player board games on his shelf. He has them numbered 1 through 10. When he plays the game i against Diego, he has a i^2/100 chance of winning. If Andrew rolls a fair ten-sided die to determine which game to play, the probability that he will win a...
ABC is a triangle with a right angle at A. M and N are points on BC such that AM is the altitude, and AN is the angle bisector of ÚBAC. If CN/NB =21 , what is CM/MB ?
Suppose x and y are real numbers and 4x+3xi+yi−43=2y+2xi−x+2yi+5i . What is the product xy .
Two point charges +q=1 ìC and −q=−1 ìC with mass m=1 g are fixed at the positions ±r ⃗ 0 with |r 0 |=1 m . The charges are released from rest at t=0 . Find the time ô in seconds at which they collide.
what is a pentagon