In the given figure , O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If anglePRQ = l and angleOPQ = m , then find l+m.
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In the given figure, 'O' is the centre of circle, PQ is a chord and the tangent PR at P makes an angle of 50
o
with PQ, then ∠POQ is equal to?
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Correct option is A)
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