9. What is the size of the ∠POQ where O is the centre of the circle?9. What is the size of the ∠POQ where O is the centre of the circle?
Answers
Answered by
7
Answer:
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
Similar questions