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A tangent is drawn to a circle of radius 6cm from a point situated at a distance of 10 cm from the centre of the circle.
The length of the tangent will be (SSC CGL 1st Sit. 2015)
The length of the tangent will be (SSC CGL 1st Sit. 2015)
- a)4 cm
- b)5 cm
- c)8 cm
- d)7 cm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A tangent is drawn to a circle of radius 6cm from a point situated at ...
AB2 + OA2 = OB2 ⇒ AB2 = OB2 = OA2
AB2 = (10)2 – (6)2 = 100 – 36 = 64
AB = 8cm
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A tangent is drawn to a circle of radius 6cm from a point situated at ...
AB2 + OA2 = OB2 ⇒ AB2 = OB2 = OA2
AB2 = (10)2 – (6)2 = 100 – 36 = 64
AB = 8cm
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A tangent is drawn to a circle of radius 6cm from a point situated at ...
Given Data:
- Radius of the circle = 6 cm
- Distance of the point from the center of the circle = 10 cm
Explanation:
To find the length of the tangent drawn from the point to the circle, we first need to understand the concept of tangents.
Concept of Tangents:
- A tangent to a circle is a line that touches the circle at exactly one point, called the point of tangency.
- The line from the center of the circle to the point where the tangent touches the circle is perpendicular to the tangent.
Calculation:
- In this case, the line from the center of the circle to the point is the hypotenuse of a right triangle.
- The radius of the circle is the perpendicular distance from the center to the tangent.
- Given that the radius of the circle is 6 cm and the distance of the point from the center is 10 cm, we can use the Pythagorean theorem to find the length of the tangent.
- Using the Pythagorean theorem, we have:
(Length of tangent)^2 = (Distance of point from center)^2 - (Radius of circle)^2
(Length of tangent)^2 = 10^2 - 6^2
(Length of tangent)^2 = 100 - 36
(Length of tangent)^2 = 64
Length of tangent = √64
Length of tangent = 8 cm
Therefore, the length of the tangent drawn from the point to the circle is 8 cm, which corresponds to option 'C'.
- Radius of the circle = 6 cm
- Distance of the point from the center of the circle = 10 cm
Explanation:
To find the length of the tangent drawn from the point to the circle, we first need to understand the concept of tangents.
Concept of Tangents:
- A tangent to a circle is a line that touches the circle at exactly one point, called the point of tangency.
- The line from the center of the circle to the point where the tangent touches the circle is perpendicular to the tangent.
Calculation:
- In this case, the line from the center of the circle to the point is the hypotenuse of a right triangle.
- The radius of the circle is the perpendicular distance from the center to the tangent.
- Given that the radius of the circle is 6 cm and the distance of the point from the center is 10 cm, we can use the Pythagorean theorem to find the length of the tangent.
- Using the Pythagorean theorem, we have:
(Length of tangent)^2 = (Distance of point from center)^2 - (Radius of circle)^2
(Length of tangent)^2 = 10^2 - 6^2
(Length of tangent)^2 = 100 - 36
(Length of tangent)^2 = 64
Length of tangent = √64
Length of tangent = 8 cm
Therefore, the length of the tangent drawn from the point to the circle is 8 cm, which corresponds to option 'C'.
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