Question

In the given figure, from an external point P, the
tangents PT and PS are drawn to a circle with
centre O and radius r. If OP 2r, show that
ZPTS = 60° and ZOST = 30°.
T
ol
1
of
P Р
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Answer 1

Step-by-step explanation:

Answer

Given: OT=OS=r and OP=2r

In ΔTOP,

sinTPO=

OP

TO

=

2r

r

=

2

1

Since, sin30

o

=

2

1

Therefore, ∠TPO=30

o

Similarly for ∠OPS=30

o

Now,

∠TPS=∠TPO+∠OPS

= 30

o

+30

o

=60

o

As we know that ∠TPS+∠TOS=180

o

So, ∠TOS=180

o

−∠TPS

= 180

o

−60

o

=120

o

Now, in ΔTOS, let ∠OST=∠OTS=x

o

Also, ∠TOS+x

o

+x

o

=180

o

120

o

+2x

o

=180

o

2x

o

=60

o

x

o

=30

o

Therefore, ∠OST=∠OTS=30

o

.

hope so it will help you!!