Math, asked by kumarxcg, 21 days ago

BE and CF CBSE 2013 5. In the given figure, PA and PB are the tangent segments to a circle with centre O. Show that the points A, O, B and P are concyclic​

Answers

Answered by anushatyagi252
3

Step-by-step explanation:

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.

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