Question : AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. If the distance between them is 2 cm, then the radius (in cm) of the circle is:
Option 1: $\frac{\sqrt{265}}{4}$
Option 2: $\frac{\sqrt{256}}{4}$
Option 3: $\frac{\sqrt{156}}{4}$
Option 4: $\frac{\sqrt{198}}{4}$
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{\sqrt{265}}{4}$
Solution : Given, AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. Let OM be perpendicular to AB and ON be perpendicular to CD. Perpendicular from the centre to a chord bisects the chord. So, AM = BM = 4 cm and CN = DN = 3 cm Let the radius of the circle be r. ON – OM = MN = 2 cm----(1) In $\triangle$OAM, OA2 = OM2 + AM2 ⇒ r2 = OM2 + 42 ----(2) In $\triangle$OCN, OC2 = ON2 + CN2 ⇒ r2 = ON2 + 32----(3) From equation 2 and 3, we get, OM2 + 42 = ON2 + 32 ⇒ ON2 – OM2 = 16 – 9 ⇒ (ON – OM)(ON + OM) = 7 ⇒ (ON + OM) = $\frac{7}{2}$----(4) Adding equation (1) and (4), we get: ⇒ ON = $\frac{11}{4}$ Substituting this value in equation (3), we get, ⇒ r2 = $(\frac{11}{4})^2$ + 32 ⇒ r2 = $\frac{265}{16}$ $\therefore$ r = $\frac{\sqrt{265}}{4}$ cm Hence, the correct answer is $\frac{\sqrt{265}}4$.
Candidates can download this e-book to give a boost to thier preparation.
Application | Eligibility | Admit Card | Answer Key | Preparation Tips | Result | Cutoff
Question : The radius of a circle is 5 cm and the length of one of its chords is 8 cm. Find the distance of the chord from the centre.
Option 1: 3 cm
Option 2: 4 cm
Option 3: 5 cm
Option 4: 2 cm
Question : The distance between two parallel chords of length 6 cm each, in a circle of diameter 10 cm is:
Option 1: 12 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 4 cm
Question : Two circles touch each other externally, having a radius of 12 cm and 8 cm, respectively. Find the length of their common tangent AB with point A on the bigger circle and B on the smaller circle.
Option 1: $8 \sqrt{6} \mathrm{~cm}$
Option 2: $8 \sqrt{3} \mathrm{~cm}$
Option 3: $12 \sqrt{3} \mathrm{~cm}$
Option 4: $12 \sqrt{6} \mathrm{~cm}$
Question : In a circle with centre O, arc CD subtends an angle of 60° at the centre of the circle whose radius is 21 cm. Calculate the length of the arc CD.
Option 1: 20 cm
Option 2: 18 cm
Option 3: 24 cm
Option 4: 22 cm
Question : A circle with centre O has a chord AB that is 20 cm in length. If the radius of the circle is 12 cm, then the area of triangle AOB is:
Option 1: $20 \sqrt{15}$ cm2
Option 2: $22 \sqrt{11}$ cm2
Option 3: $20 \sqrt{11}$ cm2
Option 4: $22 \sqrt{15}$ cm2
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile