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
