Question

what is the value of x in the circle on the right?
the value of x is \boxed{} cm.
(round to the nearest tenth as needed.)
image of a circle with center o, a tangent segment of length 8 cm, a secant segment with one part from the external point to the circle being 7 cm and the other part (the radius) being x, and the radius to the point of tangency is also x, forming a right angle at the point of tangency

Explanation:

Step1: Identify triangle type

The triangle is right-angled (marked with a right angle).

Step2: Apply Pythagorean theorem

$$x^2 + x^2 = 8^2$$
$$2x^2 = 64$$

Step3: Solve for $x^2$

$$x^2 = \frac{64}{2} = 32$$

Step4: Calculate $x$

$$x = \sqrt{32} \approx 5.65685$$

Step5: Round to nearest tenth

$$x \approx 5.6$$

Answer:

5.6 cm