By applying trigonometric reasons, Pythagorean theorem and the definition of circle arc, the measure of the arc ADC is approximately 15.858 centimeters.
How to determine the arc of a system formed by a circle and two symmetrical right triangles
Since AB and BC are tangent to the circle, then the triangles OAB and OBC are right angled. We can determine the measure of the angle AOC by using the following inverse trigonometric reason and Pythagorean theorem:
[tex]\theta = 2\cdot \tan^{-1}\left(\frac{\sqrt{10^{2}-4^{2}}}{4} \right)[/tex]
θ ≈ 132.844°
And the measure of the arc ADC is found by the formula for the length of a circle arc:
s = θ · r (1)
Where:
- θ - Central angle, in radians
- r - Radius, in centimeters
s = (2π - 132.844π/180) · (4 cm)
s ≈ 15.858 cm
By applying trigonometric reasons, Pythagorean theorem and the definition of circle arc, the measure of the arc ADC is approximately 15.858 centimeters.
To learn more on arc length: https://brainly.com/question/16403495
#SPJ1
