Tangent, secant, properties from external pointPractice Questions & MCQs
Practice Tangent, secant, properties from external point questions from Circles (Class 10 Maths) - important MCQs with answers and step-by-step solutions. Solve the sample questions below, then practice the full set free on the RankByte app.
Tangent, secant, properties from external pointQuiz - Solve & Score
Q1. an inspector standing at P, 35 metres from the centre of a water-treatment basin, pulls a rail taut so it just grazes the lip at a single point T. How long is the rail from P to T?
- A.44.8219 metres
- B.21 metres
- C.35 metres
- D.7 metres
Answer: B. 21 metres
The radius to the contact point T is perpendicular to the tangent, so triangle OTP is right-angled at T with hypotenuse OP = 35 metres and leg r = 28 metres. PT = sqrt(OP^2 - r^2) = sqrt(1225 - 784) = sqrt(441) = 21 metres.
Q2. a pilot standing at the lookout P, 53 m from the centre of a crop-circle plot, pulls a marker line taut so it just grazes the edge at a single point T. How long is the marker line from the lookout P to T?
- A.25 m
- B.45 m
- C.59.9416 m
- D.53 m
Answer: B. 45 m
The radius to the contact point T is perpendicular to the tangent, so triangle OTP is right-angled at T with hypotenuse OP = 53 m and leg r = 28 m. PT = sqrt(OP^2 - r^2) = sqrt(2809 - 784) = sqrt(2025) = 45 m.
Q3. a farmer standing at the anchor P, 26 m from the centre of a sprinkler arc, pulls a hose taut so it just grazes the boundary at a single point T. How long is the hose from the anchor P to T?
- A.27.8568 m
- B.24 m
- C.26 m
- D.16 m
Answer: B. 24 m
The radius to the contact point T is perpendicular to the tangent, so triangle OTP is right-angled at T with hypotenuse OP = 26 m and leg r = 10 m. PT = sqrt(OP^2 - r^2) = sqrt(676 - 100) = sqrt(576) = 24 m.
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Where can I practise Tangent, secant, properties from external point questions for Class 10 Maths?
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Are these Tangent, secant, properties from external point questions important for the exam?
Yes. These Tangent, secant, properties from external point important questions follow the Maths exam pattern (CBSE Boards, plus JEE and NEET foundation), so they help with both school and competitive prep.
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