Question

Прямая АВ касается окружности с центром О радиуса r в точке В.найдите АВ,если ОА равно2 см,а r равно 1,5 см?

Answer 1

Из прямоугольного треугольника ВОА , где угол В - прямой. По теореме Пифагора: АВ=√4-2,25=√1,75

Answer 2

Problem Analysis

We are given that line segment AB is tangent to a circle with center O and radius r at point B. We need to find the length of AB when OA is 2 cm and r is 1.5 cm.

Solution

To solve this problem, we can use the properties of tangents to a circle. When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. Therefore, triangle OAB is a right triangle.

We are given that OA = 2 cm and r = 1.5 cm. Let's use the Pythagorean theorem to find the length of AB.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the other two sides (OA and OB).

Let's denote the length of AB as x. Using the Pythagorean theorem, we have:

OA^2 + OB^2 = AB^2

Substituting the given values:

2^2 + 1.5^2 = x^2

Simplifying:

4 + 2.25 = x^2

6.25 = x^2

Taking the square root of both sides:

x = √6.25

x = 2.5 cm

Therefore, the length of AB is 2.5 cm.

Answer

The length of AB is 2.5 cm.