Question

Angle bcd is a circumscribed angle of circle a. What is the length of line segment ac?

Answer 1

Step-by-step explanation:

Answer:

The length of segment AC is 10 units ⇒ 1st answer

Step-by-step explanation:

Look to the attached figure

In circle A

∵ AB is a radius

∵ BC is a tangent to circle A at B

- The radius and the tangent are perpendicular to each other

    at the point of contact

∴ AB ⊥ BC at point B

∴ m∠ABC = 90°

In ΔABC

∵ m∠B = 90°

∵ AB = 8 units

∵ BC = 6 units

- By using Pythagoras Theorem (Square the hypotenuse is

    equal to the sum of the squares of the other two sides of

     the triangle)

∵ (AC)² = (AB)² + (BC)²

∴ (AC)² = (8)² +(6)²

∴ (AC)² = 64 + 36

∴ (AC)² = 100

- Take √ for both sides

∴ AC = 10 units

The length of segment AC is 10 units

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