Circles And Lines — Practice Quiz
Kerala Board · Class 10 · Mathematics
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Quick Quiz: Circles And Lines
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Two chords AB and CD of a circle intersect at point P inside the circle. If AP = 3 cm, PB = 4 cm, and CP = 2 cm, find PD.
In a circle, a diameter is divided by a perpendicular chord into segments of 2 cm and 8 cm. What is the length of half the perpendicular chord?
A line from point P outside a circle intersects the circle at points X and Y. If PX = 4 cm, PY = 9 cm, and another line from P is tangent to the circle at T, find PT.
Two chords of lengths 8 cm and 6 cm intersect inside a circle. If one chord is divided into segments of 2 cm and 6 cm, how is the other chord divided?
Sample Questions
Which of the following statements about intersecting chords are correct?
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Product of segments of one chord equals product of segments of other chord, The relationship is AP × PB = CP × PD, The theorem applies when chords intersect inside the circle
The intersecting chords theorem states that when two chords intersect inside a circle, the product of the segments of each chord are equal. This applies to any chords, not just diameters, and the intersection point can be anywhere inside the circle, not necessarily the center.
In a circle of radius 5 cm, a point P is 3 cm from the center. If a chord passes through P, what is the product of the segments?
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16
Step 1: For point inside circle: product = r² - d². Step 2: r = 5 cm, d = 3 cm. Step 3: Product = 5² - 3² = 25 - 9 = 16. This is true for any chord through point P inside the circle.
Which measurements are needed to find the diameter of a circular ring from an arc?
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Height of the arc above the chord, Length of the chord
To find the diameter using the chord method, we need the chord length and the height (sagitta) of the arc. These create a perpendicular chord situation where the diameter is divided by the chord, allowing us to use the product theorem.
A rectangle has area 20 sq cm. Using the chord intersection principle, if we want a rectangle with the same area but width 5 cm, what should be the length?
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4 cm
Step 1: Area = length × width = 20 sq cm. Step 2: If new width = 5 cm, then new length = 20 ÷ 5 = 4 cm. Step 3: The chord intersection method helps construct this geometrically without calculation. The products of segments equal the area.
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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