# Circle question

• December 8th 2009, 04:12 AM
deltaxray
Circle 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.

• December 8th 2009, 06:25 AM
Amer
Quote:

Originally Posted by deltaxray
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.

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 $\cos A = \frac{5}{8}$

$A = \cos ^{-1} \frac{5}{8}$
A is the angle between the sides 8,5

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