BB_1 is the angle bisector of triangle ABC, and I is its incenter. The perpendicular bisector of segment AC intersects the circumcircle of triangle AIC at D and E. Point F is on the segment B_1C such that AB_1=CF. Prove that the four points B, D, E and F are concyclic.

Which elements in the set below are integers? 12, –3⁄4,√ 25 , –7, √ 5 , 14⁄7, 9 a. 12, √ 25 , –7, 9 b. 12, √ 25 , –7, 14⁄7, 9 c. –3⁄4, 25 , √ 5 ,14⁄7 d. 12, –7, 9

For the rule of 78, for a 12-month period, the last term in the sequence is 12 and the series sums to 78. for an 10 month period, the last term is and the series sum is . for a 15 month period, the last term is and the series sum is . for a 20 month period, the last term is and the series sum is

The measure of one angle of an octagon is two times smaller that of the other seven angles. what is the measure of each angle?