Can you ? having a hard time figuring this out.
seg ment h m is the diameter of circle o.
se cant a h intersects circle o at point t.
seg ment a f is tangent to circle o at point f.
.fa = 21, at = 7, t m = 90, and t h = x.
none of the angle measures are given.

3a. solve for x. show your work. (4 points)

3b. what is the measure of angle htm? explain how you know. (3 points)

3c. based on your answers to 3a and 3b, what is the radius of circle o? show your work. (3 points)

3a) The value of  x = 56

3b) The measure of ∠ H T M = 90°

3c) The radius of the circle = 53

Step-by-step explanation:

3a) ∵ A F is a tangent to the circle O at point F

∵ Secant AH intersects circle O at point T

∴ (A F)² = (A T)(A H)

∴ 7( x + 7) = (21)² ⇒ ÷ 7

∴ x + 7 = 63

∴ x = 63 - 7 = 56

3b) ∵ HM is a diameter

∴ The measure of the arc HM = 180° ⇒ semi-circle

∵ ∠ H T M is inscribed angle subtended by the arc HM

∴ m ∠ H T M = half the measure of arc HM

∴ m ∠ H T M = 180° ÷ 2 = 90°

3c) ∵ Δ H T M is a right angle triangle at T

∴ (H M)² = (M T)² + (H T)² ⇒ Pythagorean theorem

∴ (H M)² = (90)² + (56)²

∴ (H M)² = 11236

∴ HM = = 106

∴ OM = 106 ÷ 2 = 53

∵ OM is the radius of the circle O

∴ The radius  = 53

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