Prove that the length of the tangents drawn from an external point to

1.	Prove that the length of the tangents drawn from an external point to a circle are equal.
Answer» Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.To prove: PA = PBConstruction: Join OA, OB, and OP.It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.OAPA and OBPB\xa0... (1)InOPA andOPB:OAP =OBP\xa0(Using (1))OA = OB\xa0(Radii of the same circle)OP = OP\xa0(Common side)Therefore,OPAOPB\xa0(RHS congruency criterion)PA = PB(Corresponding parts of congruent triangles are equal)Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal. See in ncert....yahan par figure draw nahi kr skte..

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