Question

Из точки А к окружности с r=5 см, проведены касательные AB и АС (В и С - точки касания). Точка D принадлежит большей из дуг BC. Найдите угол BDC, если AB= 7 см.Помогите пожалуйста!

Answer 1

вложение.............................................................

Answer 2

Finding the Angle BDC

To find the angle BDC, we can use the fact that the angle between a tangent and a chord is equal to the angle in the alternate segment. In this case, angle BDC is the angle in the alternate segment to the chord BC.

Given: - AB = 7 cm - r = 5 cm (radius of the circle)

We can use the following formula to find the angle BDC: Angle BDC = 2 * atan(AB / (2 * r))

Let's calculate the angle BDC using the given values.

Calculation

Using the given values: - AB = 7 cm - r = 5 cm

We can calculate the angle BDC using the formula: Angle BDC = 2 * atan(AB / (2 * r))

Substituting the values: Angle BDC = 2 * atan(7 / (2 * 5))

Calculating: Angle BDC ≈ 2 * atan(0.7) ≈ 2 * 35.537° ≈ 71.074°

So, the angle BDC is approximately 71.074 degrees.