Question

AB is a tangent to the circle with centre at O from an
external point A. If OA = 6 cm and OB = 3√3 cm, then the length of the
tangent is

(A)3 cm
(B)3√3 cm
(C)9 cm
(D)√33 ​

Answer 1

Answer:

(a) 3 cm

Step-by-step explanation:

(OA)²= (OB)²+ (AB)²

(6)²=(3√3)²+(AB)²

36 = 27 + (AB)²

AB² = 36-27

AB² = 9

AB = √9

AB = 3cm

Answer 2

Option A: The length of the tangent AB is 3 cm.

Given :

Length of segment OA = 6 cm

Length of segment OB = $3\sqrt{3}$ cm

To Find :

Length of the tangent in the circle

Solution :

• Given the center of the circle is at point P.
• A is an external point from which the tangent AB is drawn on the circle.
• Thus, the point B lies on the circumference of the circle
• OB segment will be the radius of the circle as O is the center and B lies on the circumference.
• As tangents are perpendicular to the radius at that point, the triangle AOB will have a right angle at B.

Thus, we can apply the Pythagorean theorem in the triangle AOB with a right angle at B :

                     $(OA)^{2} = (AB)^{2} + (OB)^{2} \\(AB)^{2} = (OA)^{2} - (OB)^{2} \\(AB)^{2} = (6)^{2} - (3\sqrt{3} )^{2} \\(AB)^{2} = 36 - (9*3)\\(AB)^{2} = 36 - 27\\(AB)^{2} = 9\\(AB) = 3$

Hence, the length of the tangent is 3 cm.

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