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The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is
- a)√7 cm
- b)7cm
- c)5 cm
- d)25 cm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The length of the tangent from a point A at a circle, of radius 3 cm, ...
In a circle, the tangent from a point outside the circle is perpendicular to the radius drawn to the point of tangency.
Let O be the center of the circle, A be the point of tangency, and B be the foot of the perpendicular from A to the radius OB.
Since OA is perpendicular to AB, triangle OAB is a right triangle.
OB is the radius of the circle, so OB = 3 cm.
AB is the length of the tangent, which is given as 4 cm.
Using the Pythagorean theorem, we can find the length of OA:
OA^2 = OB^2 + AB^2
OA^2 = 3^2 + 4^2
OA^2 = 9 + 16
OA^2 = 25
Taking the square root of both sides, we find:
OA = 5 cm
Therefore, the distance of A from the center of the circle is 5 cm.
Let O be the center of the circle, A be the point of tangency, and B be the foot of the perpendicular from A to the radius OB.
Since OA is perpendicular to AB, triangle OAB is a right triangle.
OB is the radius of the circle, so OB = 3 cm.
AB is the length of the tangent, which is given as 4 cm.
Using the Pythagorean theorem, we can find the length of OA:
OA^2 = OB^2 + AB^2
OA^2 = 3^2 + 4^2
OA^2 = 9 + 16
OA^2 = 25
Taking the square root of both sides, we find:
OA = 5 cm
Therefore, the distance of A from the center of the circle is 5 cm.
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The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle isa)√7 cmb)7cmc)5 cmd)25 cmCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle isa)√7 cmb)7cmc)5 cmd)25 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle isa)√7 cmb)7cmc)5 cmd)25 cmCorrect answer is option 'C'. Can you explain this answer?.
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