Square ABCD is inscribed in circle P, with a diagonal that is 18 centimeters long. Find the exact length of the apothem of squar
2 answers:
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Answer:
see explanation
Step-by-step explanation:
a
The tangent and the radius at the point of contact form a right angle
Using Pythagoras' identity on the right triangle formed.
Let x be the distance from the centre to P, then
x² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )
x = ≈ 10.77 cm (to 2 dec. places )
b
let the required angle be Θ, then
Using the sine or cosine ratio in the right triangle.
cosΘ = =
Θ = (
) ≈ 21.8°