Question

Math help please!!!!! If AO = 21 and BC = 14, what is AB?

Answer 1

The answer is 28 because line BO is similar to AB 

Answer 2

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 = $\sqrt{784} =28$

⇒ AB = 28 units.

Hence, final answer is AB = 28 units.