Question

Отрезок АВ=48 касается окружности радиуса 14 с центром О в точке В. Окружность пересекает отрезок АО в точке D. Найдите AD ...

Answer 1

Треугольник АВО прямоугольный.
Th Пифагора:
АО^2=BO^2+AB^2
AO^2=196+2304
AO^2=2500
AO=50
Квадрат отрезка касательной равен произведению отрезков секущей.
АВ = касательная
АО = секущая
АВ^2=AO*AD
AD=AB^2/AO
AD=2304/50=46.08

Answer 2

Solution for Finding AD

To find the length of AD, we can use the fact that AB is tangent to the circle at point B, and the circle intersects segment AO at point D. Given that AB = 48 and the radius of the circle is 14, we can calculate the length of AD.

Step 1: Using the fact that AB is tangent to the circle at point B, we know that AD = DB.

Step 2: We can use the Pythagorean theorem to find the length of AD. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Step 3: Let's calculate the length of AD using the Pythagorean theorem.

Step 4: AD^2 + DB^2 = AB^2 AD^2 + AD^2 = 48^2 2(AD^2) = 48^2 AD^2 = (48^2)/2 AD = sqrt((48^2)/2)

Step 5: Calculating the value of AD: AD = sqrt((48^2)/2) AD ≈ 33.94

So, AD ≈ 33.94.