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Question

A chord of a circle makes an angle of \(90^\circ\) at the centre of the circle. If the area of the major segment is \(k\) times the area of the minor segment, then what is the value of \(k\)? (Take \(\pi = \frac{22}{7}\))

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is

\(10\)

Let radius \(= r\). Minor segment area \(=\) sector area \(-\) triangle area \(= \frac{90}{360}\pi r^2 - \frac{1}{2}r^2\sin 90^\circ = \frac{\pi r^2}{4} - \frac{r^2}{2} = \frac{r^2(\pi - 2)}{4}\). Major segment area \(= \pi r^2 - \frac{r^2(\pi-2)}{4} = \frac{r^2(3\pi+2)}{4}\). So \(k = \frac{3\pi+2}{\pi-2}\). With \(\pi = \frac{22}{7}\): \(3\pi+2 = \frac{80}{7}\) and \(\pi-2 = \frac{8}{7}\), so \(k = \frac{80/7}{8/7} = 10\).

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Important Questions from Circles, Chords and Tangents

  1. A chord 21 cm long is drawn in a circle of diameter 25 cm. The perpendicular distance of the chord from the centre is:

  2. AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 112°, then what is the measure of ∠OAB ?

  3. In a circle with radius 5 cm, a chord is at a distance of 3 cm from the centre. The length of the chord is:

  4. The distance between the centres of two circles is 24 cm. If the radius of the two circles are 4 cm and 8 cm, then what is the sum of the lengths (in cm) of the direct common tangent and the transverse common tangent?

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