Line AB touches a circle with center O of radius 2 cm at point A, so OA = AB. What is the OB segment equal to?

Given:

circle centered at point O,

tangent AB,

OA = 2cm,

OA = OB.

It is required to find the OB

ОВ -?

Solution :

By connecting points O, A and B, we get a triangle. this triangle will be rectangular. Because a tangent with a radius drawn to the tangent point forms a right angle.

Side ОА = 2 cm (according to the problem statement).

We also know that OA = AB. Therefore AB = 2cm.

OA and AB will be the legs of a right-angled triangle. Let’s find the hypotenuse, through the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs.

OB = root of 2² + 2² = root of 4 + 4 = root of 8.

Answer: OB = square root of 8.