Question

in the given figure PT AND PS are the tangent segments to a circle with center O ,show that the points P,T,O and S are cocyclic ​

Answer 1

Answer:

From figure, PA and PB are the tangents.

O is the centre of the circle.

To Prove : AOBP is a cyclic quadrilateral

Now,

OA is radius and PA is tangent

OA⊥PA

So, ∠OAP=90

∘

___(1)

Similarly, OB is radius and PB is tangent.

OB⊥PB

So, ∠OBP=90

∘

__(2)

Add (1) and (2), we have

∠OAP+∠OBP=90

∘

+90

∘

=180

∘

But these are opposite angles of the quadrilateral AOBP.

Therefore, Quadrilateral AOBP is a cyclic quadrilateral

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