Question

please solve example 2

Answer 1

$\huge\mathfrak\orange{Hello! \: Beauty girl}$

$\huge\mathfrak\blue{Solution:-}$

$<i><b>$Given :- a circle with centre o two tangents TP and take you to the circle where p and q are the point of the contact .

To prove :- angle PTQ = to 2 Angle OPQ

proof :- length of the tangents drawn from an external point to a circle are equal .

So , angle TPQ = angle TPQ ( angle opposite to equal sides are equal ) ------ ( 1 )

Now , PT is tangents & OP is radius .

OP perpendicular TP ( tangent at any point

so ,
angle OPT = 90°
and TPQ = 90° - angle OPQ. ------( 2 )

In ∆ PTQ
ANGLE TPQ + ANGLE TQP + ANGLE PTQ = 180°
( ANGLE OF THE SUM PROPERTY ).

ANGLE TPQ + ANGLE TPQ + ANGLE PTQ = 180°

2 ( 90° - ANGLE OPQ ) + ANGLE PTQ = 180°

ANGLE = 180° - 180° + 2 ANGLE OPQ

ANGLE PTQ = 2 ANGLE OPQ

$\huge\boxed{Hense \: Proved }$

$\huge\mathfrak\green{thanks}$ .

Answer 2

follow the attachment above ⬆⬆