1.

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?

Answer»

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


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