Length of Segment in Inscribed Triangle

Hard Problem Solving Geometry

A triangle ABC is inscribed in a circle with a radius of 10 cm. Point D is the midpoint of side BC. What is the length of segment AD?

Given:

- Let α be the angle at vertex A, and let the angles at vertices B and C be β and γ, respectively. It is known that α + β + γ = 180°.

We need to determine the length of segment AD using the following statements:

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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