Question

Given circle E with diameter CD and radius EA. AB is tangent to E at A. If E A = 18 and DB = 12, solve for AB. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined."

Answer 1

Answer:

$\text{AB = 24}$

Step-by-step explanation:

$\text{Solution: }$

$\text{1. EA = ED = 18 [Radii of same circle are equal.]}$

$\text{2. EA}\perp\text{AB}\ \ \ [\text{Radius is perpendicular to tangent at the point of contact.}]\\\text{i.e. Triangle AEB is right angled triangle.}$

$\text{3. Using pythagoras theorem in triangle AEB,}\\\text{EB}^2=\text{EA}^2+\text{AB}^2\\\text{or, }(\text{ED+DB})^2=18^2+\text{AB}^2\\\text{or, }(18+12)^2=324+\text{AB}^2\\\text{or, AB}^2=900-324=576\\\text{or, AB}=\sqrt{576}\\\text{or, AB = }24$