A circle k(O) with the radius r is given. Line AB tangent to circle k(O) at B. Find AB, if OA= 2 cm, and r=1.5 cm.
Answers
Answer:
AB is 1.32 cm.
Step-by-step explanation:
A circle k(O) with the radius r is given. Line AB tangent to circle k(O) at B. Find AB, if OA= 2 cm, and r=1.5 cm.
Based on the given in the problem,
Line AB tangent to circle k(O) at B, therefore AB is perpendicular to OB and formed right angle.
Given OA = 2 cm and r = 1.5 cm, r = OB
Then, we formed a right triangle OBA with right angle at B.
Thus, finding AB as one of the legs of the right triangle, we will apply the Pythagorean Theorem.
c² = a² + b²
a² = c² - b² Deriving the formula in finding the missing leg.
a = AB, c = OA, b = OB
(AB)² = (OA)² - (OB)² Substitute the values.
(AB)² = 2² - (1.5)² Simplify the exponent.
(AB)² = 4 - 2.25 Subtract 2.25 from 4 applying rules in subtraction of decimals from a whole number
(AB)² = 1.75 Extract the square root.
√(AB)² = √1.75
AB = 1.32 cm