What is the size of the ∠POQ where o is the centre of the circle?
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Answer:
We know, that radius is perpendicular to a tangent .
∴ ∠OPR=90
o
⇒ ∠OPQ+∠QPR=90
o
⇒ ∠OPQ+50
o
=90
o
⇒ ∠OPQ=90
o
−50
o
⇒ ∠OPQ=40
o
⇒ OP=OQ [ Radii of a circle ]
⇒ ∠OPQ=∠OQP=40
o
[ Base angles of equal sides are also equal ]
In △POQ,
⇒ ∠OQP+∠POQ+∠OPQ=180
o
[ Sum of angles of a triangle is 180
o
]
⇒ 40
o
+∠POQ+40
o
=180
o
⇒ ∠POQ+80=180
o
⇒ ∠POQ=100
o
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