A point P is 8cm from the centre of a circle of radius length 5cm. Find the length of the major arc between the points of contact of the tangents drawn from P to the circle.

Thanks in advance.

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- Dec 8th 2009, 03:12 AMdeltaxrayCircle question
A point P is 8cm from the centre of a circle of radius length 5cm. Find the length of the major arc between the points of contact of the tangents drawn from P to the circle.

Thanks in advance. - Dec 8th 2009, 05:25 AMAmer
this is the graph

Attachment 14344

the arc length equal the radius multiply with the arc angle in radian

so we need to find the angle between the side 8 and the side 5, there is a theorem that said the the line joined from the center to any tangent point is orthogonal to the tangent line from that point

so the angle equal $\displaystyle \cos A = \frac{5}{8} $

$\displaystyle A = \cos ^{-1} \frac{5}{8} $

A is the angle between the sides 8,5

finally

$\displaystyle arc \; \; length = A (5) $