Hard - Quiz 1

Push your circle skills with intersecting chords, algebraic sector problems, radian-based reasoning, point-to-circle distance, and tangent-radius right triangles.

Question 1 of 5

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Question 1

Two chords intersect inside a circle. One chord is divided into segments of length 3 and 8. The other chord has one segment of length 4. What is the length of the other segment of the second chord?

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A sector of a circle has an area of \(24\pi\) square inches and a central angle of 60°. What is the radius of the circle, in inches?

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A sector of a circle has a radius of 10 centimeters and an arc length of \(5\pi\) centimeters. What is the area of the sector?

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A circle has the equation \((x - 1)^2 + (y - 3)^2 = 16\). What is the shortest distance from the point \(P(1, 8)\) to the circle?

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A circle has center \(O\) and radius 5. A point \(P\) outside the circle is 13 units from the center. A line from \(P\) is tangent to the circle at point \(T\). What is the length of \(PT\)?

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