Question 139

AB is a tangent to a circle with centre O. If the radius at the circle is 7 cm and the length of AB is 24 cm, the what is the length (in cm.) of OA ?

Solution

Given : OB is radius of circle = 7 cm and tangent AB = 24 cm

To find : OA = ?

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

Thus in $$\triangle$$ OAB,

=> $$(OA)^2=(OB)^2+(AB)^2$$

=> $$(OA)^2=(7)^2+(24)^2$$

=> $$(OA)^2=49+576=625$$

=> $$OA=\sqrt{625}=25$$ cm

=> Ans - (A)

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