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Angle BCD is a circumscribed angle of circle A.

Circle A is shown. Line segments B A and D A are radii. Tangents B C and D C intersect at point C outside of the circle. A line is drawn to connect points A and C. The length of A B is 8 and the length of B C is 6. Angle C A D is 37 degrees.

What is the length of line segment AC?

10 units
12 units
14 units
16 units

User CFUser
by
5.8k points

2 Answers

3 votes

Answer:

10 units

Explanation:

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User Tim Beaudet
by
6.0k points
3 votes

Answer:

The length of segment AC is 10 units1st answer

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

Angle BCD is a circumscribed angle of circle A. Circle A is shown. Line segments B-example-1
User Prajo
by
6.6k points