Từ điểm A ở ngoài (O) kẻ các tiếp tuyến AB, AC với đường tròn (B và C là các tiếp điểm), BC cắt OA tại D, trên cung nhỏ BC lấy E, ED cắt (O) tại F chứng minh góc BAE = góc CAF

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?

Since opening night, attendance at play a has increased steadily, while attendance at play b first rose and then fell. equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. on what day(s) was the attendance the same at both plays? what was the attendance? play a: y = 8x + 191 play b: y = -x^2 + 26x + 126 a. the attendance was never the same at both plays. b. the attendance was the same on day 5. the attendance was 231 at both plays on that day. c. the attendance was the same on day 13. the attendance was 295 at both plays on that day. d. the attendance was the same on days 5 and 13. the attendance at both plays on those days was 231 and 295 respectively.

Bob is putting books on a shelf and takes a break after filling 18 1/2 inches on the book shelf. the book shelf is now 2/3 full. how long is the entire bookshelf?