Tangent and Circle Problem
A large circle has centre C and diameter AB. A smaller circle has centre D and diameter BC. Chord AE is tangent ot the smaller circle. If AB = 18 cm, what is the exact length of AE in radical form?
The triangle AED is a right triangle with angle AED is a right angle.
DE=1/2BC and BC=1/2AB so DE=1/4AB = 18/4 cm.
CD=1/2BC and BC=1/2AB so CD=1/4AB
So `AE^2=AD^2-DE^2 = (3/4)^2(AB)^2-(1/4)^2(AB)^2=(9/16-1/16)(AB)^2`
`AE = sqrt(2)/2AB=9sqrt(2)` cm