Question 37

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

Solution

Given : OT is radius of circle = 5 cm and OP = 13 cm

To find : Tangent PT = ?

Solution : The radius of a circle intersects the tangent at right angle, => $$\angle OTP = 90^\circ$$

Thus in $$\triangle$$ OPT,

=> $$(PT)^2=(OP)^2-(OT)^2$$

=> $$(PT)^2=(13)^2-(5)^2$$

=> $$(PT)^2=169-25=144$$

=> $$PT=\sqrt{144}=12$$ cm

=> Ans - (C)

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