Question

In the given figure, PT and PS are the tangents to the circle form a point P such that PT =4cm and /_ TPS = 60° find the length of chord TS. How many such line of same length TS can be drawn in the circle?

Answer 1

wkt pt and ps are equal as they are tangents from same external point

thus angle PTS=angle PST.....1
(angles opposite to equal sides)

in triangle PTS
ang P +S+T=180
(asp)
60 +P+P=180
shows P=60
thus S=60
since all angel s are 60
PTS is an equilateral triangle
thus PT=TS=4cms

Answer 2

$ps = pt \: \\ (when \: two \: tangents \: met \: at \: a \: point \: externally \: then \: their \: lenghts \: are \: equal$
$therefore$
$< pts = < pst \: angle \: opp \: to \: equal \: sides \: are \: equal$
now in triangle PTS
$< PTS + < PST + < TPS=180$
$< PTS+ < PTS+60=180$
$2 < pts = 180 - 60$
$< PTS =60 \\ < PSt =60$
therefore all angles are 60 degree it means it is an equilateral triangle

and we know that sides of equilateral triangle are equal
$so \: the \: cord \: TS \: is \: of \: 5cm$