# 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 isA. 3 cmB. 4 cmC. 5 cmD. 6 cm

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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