Question

Can you help? Having a hard time figuring this out. Thanks

Answer 1

Answer:

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 = $\sqrt{11236}$ = 106

∴ OM = 106 ÷ 2 = 53

∵ OM is the radius of the circle O

∴ The radius  = 53