A tangent from point P to a circle of radius 4 cm is 10 cm long. Find:a the distance of P from the centre of the circleb the size of the angle between the tangent and the line joining P to the centre of thecircle.
Accepted Solution
A:
Answer:see explanationStep-by-step explanation:aThe tangent and the radius at the point of contact form a right angleUsing Pythagoras' identity on the right triangle formed.Let x be the distance from the centre to P, thenx² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )x = [tex]\sqrt{116}[/tex] ≈ 10.77 cm (to 2 dec. places )blet the required angle be Θ, thenUsing the sine or cosine ratio in the right triangle.cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10}{\sqrt{116} }[/tex]Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{10}{\sqrt{116} }[/tex] ) ≈ 21.8°