Circles MCQs

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.