All Exams Test series for 1 year @ ₹349 only
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 \(k = \frac{80/7}{8/7} = 10\).

Was this answer helpful?

Similar Questions

  1. An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. what is ∠BDC equal to?

  2. What is the length of QC ?

  3. What is the relation between x and y ?

  4. If y = 15, then what is ∠ACB equal to ?

  5. If r is the radius of S and R is the radius of S2, then which one of the following is correct?

  6. If m is the area of the circle S and n is the area of semi-circle S1, then which one of the following is correct?

  7. A circle is inscribed in a triangle ABC. It touches the sides AB and AC at M and N respectively. If O is the centre of the circle and ∠A = 70°, then what is ∠MON equal to?

  8. If ∠ABD = θ, then what is sin θ equal to ?  

  9. What is the radius of the circle ?

  10. What is the radius of the circle ?


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. 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?

  4. An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. what is ∠BDC equal to?

  5. In a circle with centre O, an arc ABC subtends an angle of 132° at the center of the circle. Chord AB is produced to point P. Then ∠CBP is equal to∶

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
536 Tests 4 Tests Free
1693 Attempts
4.3(174)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App