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Masteriza [31]
3 years ago
14

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 circle

>b the size of the angle between the tangent and the line joining P to the centre of the
circle.
Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
7 0

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 = \sqrt{116} ≈ 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 = \frac{adjacent}{hypotenuse} = \frac{10}{\sqrt{116} }

Θ = cos^{-1} ( \frac{10}{\sqrt{116} } ) ≈ 21.8°

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