Question

In circle A as shown below, segment DC is tangent to circle A at D.

Answer 1

Answer:

3 units

Step-by-step explanation:

Let the radius be x

Therefore, using pythagoras Theorem,

${4 {}^{2} + {x}^{2} } = (x + 2) {}^{2} \\ 16 + x {}^{2} = {x}^{2} + 4x + 4 \\ 4x + 4 = 16 \\ 4x = 12 \\ x = 3$

Answer 2

Answer:

AB = 3

Step-by-step explanation:

AB = AD

AB² + 4² = (AB + 2)²

AB² + 16 = AB² + 4AB + 4

combine like terms:

4AB = 12

AB = 3