Class 10 Exam > Class 10 Questions > In a circle of radius 7cm, tangent PT is draw...
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In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:
- a)30cm
- b)31cm
- c)28cm
- d)25cm
Correct answer is option 'D'. Can you explain this answer?
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In a circle of radius 7cm, tangent PT is drawn from point P such that ...
Understanding the Problem
In this problem, we need to find the length of OP, where O is the center of the circle, P is the external point from which the tangent PT is drawn, and PT is the tangent line to the circle.
Given Information
- Radius of the circle (r) = 7 cm
- Length of the tangent (PT) = 24 cm
Using the Tangent-Secant Theorem
According to the tangent-secant theorem, the length of the tangent from an external point to a circle is given by:
OP² = OT² + PT²
Where:
- OP is the distance from the center of the circle to the external point P.
- OT is the radius of the circle (7 cm).
- PT is the tangent length (24 cm).
Calculating OP
1. Calculate OT (the radius):
OT = 7 cm
2. Calculate PT:
PT = 24 cm
3. Apply the theorem:
OP² = OT² + PT²
OP² = (7)² + (24)²
OP² = 49 + 576
OP² = 625
4. Find OP:
OP = √625
OP = 25 cm
Conclusion
Thus, the length of OP is 25 cm. Therefore, the correct answer is option 'D'.
In this problem, we need to find the length of OP, where O is the center of the circle, P is the external point from which the tangent PT is drawn, and PT is the tangent line to the circle.
Given Information
- Radius of the circle (r) = 7 cm
- Length of the tangent (PT) = 24 cm
Using the Tangent-Secant Theorem
According to the tangent-secant theorem, the length of the tangent from an external point to a circle is given by:
OP² = OT² + PT²
Where:
- OP is the distance from the center of the circle to the external point P.
- OT is the radius of the circle (7 cm).
- PT is the tangent length (24 cm).
Calculating OP
1. Calculate OT (the radius):
OT = 7 cm
2. Calculate PT:
PT = 24 cm
3. Apply the theorem:
OP² = OT² + PT²
OP² = (7)² + (24)²
OP² = 49 + 576
OP² = 625
4. Find OP:
OP = √625
OP = 25 cm
Conclusion
Thus, the length of OP is 25 cm. Therefore, the correct answer is option 'D'.
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In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:a)30cmb)31cmc)28cmd)25cmCorrect answer is option 'D'. 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 In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:a)30cmb)31cmc)28cmd)25cmCorrect answer is option 'D'. 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 In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:a)30cmb)31cmc)28cmd)25cmCorrect answer is option 'D'. Can you explain this answer?.
In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:a)30cmb)31cmc)28cmd)25cmCorrect answer is option 'D'. 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 In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:a)30cmb)31cmc)28cmd)25cmCorrect answer is option 'D'. 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 In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:a)30cmb)31cmc)28cmd)25cmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:a)30cmb)31cmc)28cmd)25cmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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