Question

The length of two tangents of a circle from a point is 30 cm each

Answer 1

Answer:

Given, radius of the circle is √3 cm. We know that two tangents drawn to a circle from an external point are equally inclined to the segment joining the center to the point. Again, OA is perpendicular to AP and OB is perpendicular to BP. So, PA = PB = 3 cm...........................

Answer 2

The distance between the point and center of circle=$20\sqrt 3cm$

Step-by-step explanation:

Length of each tangent of  a circle=30 cm

Angle between two tangents, angle P=60 degrees

We know that

When a line drawn from external point of circle to the center then it will bisect the angle formed at center and angle formed between two tangents.

Angle OPA=$\frac{1}{2}\angle P=\frac{1}{2}(60)=30^{\circ}$

Radius is always perpendicular to tangent therefore, triangle OPA is a right triangle.

PA=30 cm

$\frac{PA}{OP}=cos\theta=\frac{Base}{Hypotenuse}$

$\frac{30}{OP}=cos 30^{\circ}$

$\frac{30}{OP}=\frac{\sqrt 3}{2}$

Because $cos 30^{\circ}=\frac{\sqrt 3}{2}$

$OP=\frac{30\times 2}{\sqrt 3}=\frac{60\sqrt 3}{\sqrt 3\times \sqrt 3}$

$OP=\frac{60\sqrt 3}{3}=20\sqrt 3cm$

Hence, the distance between center and point P=$20\sqrt 3cm$

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