Q. 235.0( 5 Votes )

In the given figure, PA and PB are two tangents drawn from an external point P to a circle with center C and radius 4 cm. If PA PB, then the length of each tangent is


A. 3 cm

B. 4 cm

C. 5 cm

D. 6 cm

Answer :


Join AC, BC and CP


To Find: Length of tangents


Now,


PA = PB…[1]


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


In ACP and BCP


PA = PB [By 1]


CP = CP [Common]


CA = CB [radii of same circle]


ACP ≅△BCP [By Side - Side - Side Criterion]


CPA = CPB


[Corresponding parts of congruent triangles are congruent]


Now,


APB = 90°


[Given that PA PB]


CPA + CPB = 90°


CPA + CPA = 90°


2 CPA = 90°


CPA = 45°


In ACP


CA PA [Tangents drawn at a point on circle is perpendicular to the radius through point of contact


ACP is a right - angled triangle.


So, we have





PA = 4 cm


From [1]


PA = PB = 4 cm


i.e. length of each tangent is 4 cm

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