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line AB is tangent to circle O at A. The diagram is not drawn to scale.

If AO=21 and BC=14, what is AB?

line AB is tangent to circle O at A The diagram is not drawn to scale If AO21 and BC14 what is AB class=

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Matheng
AO = 21
BC = 14
OC = radius of the circle = AO = 21
∴ OB = OC + CB = 21 + 14 = 35
Line AB is tangent to circle O at A
∴ AB is perpendicular to AO
∴ Δ OAB is a right triangle at A
Applying Pythagorean theorem
∴  OB² = AO² + AB²
∴ AB² = OB² - AO² = 35² - 21² = 1225 - 441 = 784
∴ AB = √784 = 28

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