Given is a circle O with tangent AB and secant OB.
Given is OA = 21 units and BC = 14 units.
From the diagram, OB = OC + BC.
OC and OA, both are radius, so OC = OA = 21 units.
Now OB = 21 + 14 = 35 units.
In right triangle ΔOAB, using Pythagorean theorem;
OA² + AB² = OB²
⇒ (21)² + AB² = (35)²
⇒ 441 + AB² = 1225
⇒ AB² = 1225 - 441 = 784 square units
⇒ AB = [tex]\sqrt{784} =28[/tex]
⇒ AB = 28 units.
Hence, final answer is AB = 28 units.
