Question

Prove that tangents drawn at the ends of a diameter of a circle are parallel

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

● AB,CD are two tangents at the ends of a diameter PQ in circle with centre O⠀⠀⠀

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

$\pink{AB\parallel{CD}}$⠀⠀⠀⠀

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

If APB is the tangent and OP joined,

$\therefore{\pink{OP⊥{AB}}}$

similarly,

$\therefore{\pink{OQ⊥ {CD}}}$

$\rightsquigarrow{\angle{APQ}=90°}$

$\rightsquigarrow{\angle{CQP}=90°}$

$\implies{\angle{APQ}+\angle{CQP}=90°+90°=180°}$

$\textsf{But there are co-interior angle}$

so,

$\rightsquigarrow$$\orange{AB\parallel{CD}}$

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$⠀⠀⠀⠀

☆The tangents drawn at the ends of a diameter of a circle are parallel,$\tt{\red{\underline{\overline{《Proved》}}}}$