Question

Из точки наибольшее расстояние которой до окружности равно 50мм проведена касательная, отрезок касательной между точкой касания и данной точкой равен 40мм.Найти диаметр окружности.

Answer 1

Треугольник АОВ равнобедр т к АО=ОВ радиусы значит угол А=углу В 180-70=110 110/2=55 ВАС=55

Answer 2

Problem Analysis

We are given that there is a point outside a circle, and the distance from that point to the circle is 50mm. A tangent is drawn from that point to the circle, and the length of the tangent segment between the point of tangency and the given point is 40mm. We need to find the diameter of the circle.

Solution

Let's assume that the center of the circle is O, the point outside the circle is P, and the point of tangency is T. We can form a right triangle OPT, where OT is the radius of the circle, PT is the tangent segment, and OP is the distance from the point to the circle.

Using the Pythagorean theorem, we can write the equation: OP^2 = OT^2 + PT^2

We are given that OP = 50mm and PT = 40mm. Let's substitute these values into the equation: 50^2 = OT^2 + 40^2

Simplifying the equation: 2500 = OT^2 + 1600

Rearranging the equation: OT^2 = 2500 - 1600 OT^2 = 900

Taking the square root of both sides: OT = √900 OT = 30

Since OT represents the radius of the circle, the diameter of the circle is twice the radius: Diameter = 2 * OT Diameter = 2 * 30 Diameter = 60

Therefore, the diameter of the circle is 60mm.

Answer

The diameter of the circle is 60mm.