Question

In the adjoining figure, PA are PB and two tangents drawn from an external point P to a circle with centre C and radius 4cm.if PA perpendicular PB ,then find the length of each tangent.

Answer 1

Solution:

Keep in mind:

1. Length of tangents from external point to a circle are equal.

2. The line joining from center of circle to point of contact of tangent makes an angle of 90° with the tangent .

In ΔPAC and ΔPBC

∠PAC=∠PBC=90° -----Reason written in 2

CA=CB→→Radii of circle

PA=PB------Reason written in 1.

ΔPAC ≅ ΔPBC →→[SAS]

∠APC=∠BPC=45°[CPCT]

AS, PA ⊥ PB

So, ∠APB=90°

2 ∠APC=90°

∠APC=45°

In ΔCAP, Right angled at A

tan 45°

$=\frac{AC}{AP}\\\\1=\frac{4}{AP}\\\\ AP=4 cm$

So, PA=PB=4 cm