Question

Show that the lengths of tangents drawn from an external point to a circle are equa​

Answer 1

Answer:

Hey!! Here is your answer.....

Statement :- The lengths of tangents drawn from an external point to a circle are equal.

Given :- A circle with centre o, p is a point lying outside the circle and PA and PB are two tangents to the circle from p.

To prove :-PA=PB.

Proof :- Join OA, OB and OP.

Angle OBP = Angle OAP = 90

(Angle between tangent and radius is 90)

Now in ∆OAP and in ∆OBP

OA = OB(radii of the same circle)

OP=OP

∆OAP congruent ∆ OBP(R. H. S congruence)

:. PA=PB ( CPCT)

Hence proved.

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