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Is the following statement true or false?

$PA$ and $PB$ are the tangents to a circle with centre $O$ , then the points $A, O, B, P$ are not concyclic.

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True

False

answer is B.

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Detailed Solution

Given that,
Question Image

PA

and

PB

are the tangents to a circle

O

.
Computing that the points

A, O, B

, and P are concyclic.

∴ O B ⊥ P B and O A ⊥ A P

∠ OBP = 90 °, ∠ OAP = 90 °

Computing further,

∠ O B P + ∠ O A P = 90 + 90 = 180 °

The sum of the opposite angles in a quadrilateral is

180 °

, therefore it is a cyclic quadrilateral.
A, O, B and P are concyclic.
Thus, the given statement is false and the correct statement is,
‘

PA

and

PB

are the tangents to a circle with centre

O

, then the points

A, O, B, P

are concyclic.’
Therefore the correct option is 2.

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