Question

In the figure given below, AR is a tangent to the circle. AM is the secant. Find the length of PM, if AR = 6 cm and AP = 2 cm.

$\left[2Marks\right]$

Answer 1

Given: AR = 6 cm, AP = 2 cm. AR is a tangent at R.

We know that, if a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
i.e. AP x AM = $(AR{)}^2$
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$\Rightarrow 2\times (AP+PM)=(AR{)}^2\Rightarrow 2\times (2+PM)=6^2$
$\Rightarrow$ 2 x (2 + PM) = 36
(2 + PM) = 18 $\therefore$ PM = 16
$\left[1Mark\right]$