Problem: On hypotenuse ABA BAB of a right triangle ABCA B CABC a second right triangle ABDA B DABD is constructed with hypotenuse ABA BAB. If BC=1,AC=bB C=1, A C=bBC=1,AC=b, and AD=2A D=2AD=2, then BDB DBD equals:
Answer Choices:
A. b2+1\sqrt{b^{2}+1}b2+1β
B. b2β3\sqrt{b^{2}-3}b2β3β
C. b2+1+2\sqrt{b^{2}+1}+2b2+1β+2
D. b2+5b^{2}+5b2+5
E. b2+3\sqrt{b^{2}+3}b2+3β Solution:
x2+4=b2+1x^{2}+4=b^{2}+1 x2+4=b2+1
β΄x=b2β3\therefore x=\sqrt{b^{2}-3} β΄x=b2β3β