Tangent, secant, properties from external point MCQs
Practice Tangent, secant, properties from external point multiple-choice questions from Circles (Class 10 Maths) - tap an answer for instant feedback and a step-by-step solution. 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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