Problem: In a circle with center OOO chord AB=A B=AB= chord ACA CAC. Chord ADA DAD cuts BCB CBC in EEE. If AC=12A C=12AC=12 and AE=8A E=8AE=8, then ADA DAD equals:
Answer Choices:
A. 272727
B. 242424
C. 212121
D. 202020
E. 181818 Solution:
△AEB∼△ABD\triangle \mathrm{AEB} \sim \triangle \mathrm{ABD} △AEB∼△ABD
AD12=128AD=18\dfrac{A D}{12}=\dfrac{12}{8} \quad A D=18 12AD​=812​AD=18