Question

AB is a chord of length 9.6cm of a circle with centre O and radius 6 cm. If the tangents at A and B intersect at point P then find the length PA.

Answer 1

Hope it will help you.

Answer 2

OP is the perpendicular Bisector of chord AB

$\therefore$ $\sf{AR=BR=\frac{1}{2}AB}$

$\longrightarrow$$\sf{\frac{1}{2}=9.6=4.8cm}$

$\sf{In\:right\:∆ARO,we\:have}$

$\longrightarrow$$\sf\red{OR = \sqrt{ {or}^{2} - {AR}^{2} }}$

$\longrightarrow$$\sf\red{ \sqrt{ {6}^{2} - {(4.8)}^{2} }}$

$\longrightarrow$$\sf\red{\sqrt{10.8 \times 1.2}}$

$\longrightarrow$$\sf\red{\sqrt{12.96}}$

$\longrightarrow$$\sf\red{3.6cm}$

$\sf\purple{∆ARP~∆ORA}$

$\therefore$ $\sf\blue{\frac{PA}{AR}=\frac{OA}{OR}}$

Hence, $\sf\blue{PA=\frac{OA}{OQ}×AR}$

$\sf{\frac{6×4.8}{3.6}=8cm}$