what is the size of the angle POQ where O is the center of the circle
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Given that, O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50
o
with PQ.
We need to find ∠POQ.
We know that the tangent is perpendicular to the radius.
∴∠OPQ+∠QPR=90
o
From the figure ∠QPR=50
o
.
⇒∠OPQ+50
o
=90
o
⇒∠OPQ=90
o
−50
o
∴∠OPQ=40
o
We know that, the angles opposite to the equal sides of the triangle are equal.
∴∠OPQ=∠OQP=40
o
Also, we know that sum of angles in the triangle is 180
o
.
⇒∠OPQ+∠OQP+∠POQ=180
o
⇒40
o
+40
o
+∠POQ=180
o
⇒80
o
+∠POQ=180
o
⇒∠POQ=180
o
−80
o
∴∠POQ=100
o
Answered by
20
Answer:
answer is 124
Step-by-step explanation:
by using theorem 10.8 (check on class 9th maths text book theorem 10.8)
so angle poq = 2(62)
= 124
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