Question

PA and PB are two tangents drawn to circle of radius 4 centimetre from external point P.PA is perpendicular to PB then find the length of the tangent​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

${\huge\tt{Given}}\begin{cases}\sf{PA\:and\:PB\:are\:tangents}\\\sf{radius = 4\:cm}\\ \sf{PA\perp PB} \end{cases}$

$\huge\tt {TO\:FIND:-}$

• Length of tangent

$\huge \tt {SOLUTION:-}$

In $\tt {\triangle CAP\:and\: \triangle CBP}$,

• $\tt {\angle A= \angle B}$ (radius are perpendicular to tangent)
• $\tt {CP=CP}$ (common)
• $\tt {CA=CB}$ (radius)

$\tt{ Thereore,\:By\:RHS,}$

$\huge{\boxed {\tt \triangle CAP \cong \triangle CBP}}$

So,

$\tt{\angle APC = \angle BPC = 45^{\circ} }$

Even,

$\tt{\angle ACP = \angle BCP = 45^{\circ} }$

$\huge {\boxed{\tt AC=AP,CB=CP}}$

$\tt \therefore It\:is\:a\:square.$

The radius was 4 cm.

Since, it's a square.

$\huge {\boxed {\tt AC=BC=AP=BP=4 \:cm}}$

So, the tangent's measure is 4 cm.

$\rule{200}2$