The circumference C of a circle is given by C = πd. Thus, C = π(14) ≈ 44 cm.

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Thus, (4/8)² = 1/4.

Using the Pythagorean theorem, if PQ² + PR² = QR², then it is a right triangle. 8² + 6² = 64 + 36 = 100 = 10².

Since the triangles are similar, corresponding angles are equal. Therefore, angle X = angle D = 30 degrees.

The circumference C of a circle is given by C = 2πr. Thus, r = C / (2π) = 31.4 / (2π) ≈ 5 cm.

Using the tangent-secant theorem, PT² = PO² - OT². Thus, PT² = 13² - 5² = 169 - 25 = 144, so PT = 12 cm.