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kicyunya [14]
3 years ago
14

In the figure below, the segment that appears to be tangent to the circle is tangent to the circle. Which of the following is th

e length of the diameter of the circle to the nearest tenth of a unit?
A. 41.7

B. 26.7

C.16.0

D. 9.0

Mathematics
1 answer:
maria [59]3 years ago
6 0

Answer:

Step-by-step explanation:

Check attachment for diagram,

Since line AB is tangent to the circle then, <OAB is a right angle,

Then, we can apply Pythagoras theorem to the right angle triangle,

NOTE: from the centre of the circle to the tangent point at A is the radius of the circle,

And also, the total length of OB is

OB = r + 15

Then, applying Pythagorean theorem

OB² = OA² + AB²

(r+15)² = r² + 25²

(r+15)(r+15) = r² + 625

r² + 15r + 15r + 225 = r² + 625

Collect like terms

r² + 30r - r² = 625 - 225

30r = 400

Divide both sides by 30

r = 400 / 30

r = 13.33

So, the diameter of the circle is related to the radius by the relation

Diameter = 2 × radius

d = 2 × r

d = 2 × 13.33

d = 26.67

To the nearest tenth implies that to 1d•p

d ≈ 26.7

So, the diameter of the circle is 26.7

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