Question : Two equal circles of radius 6 cm intersect each other such that each passes through the centre of the other. The length (in cm) of the common chord is:
Option 1: $5 \sqrt{3}$
Option 2: $6 \sqrt{3}$
Option 3: $4 \sqrt{3}$
Option 4: $3 \sqrt{3}$
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
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: $6 \sqrt{3}$
Solution : Let the common chord AB bisect the distance between the centre XY at O. ⇒ XO = $\frac{\text{XY}}{2}$ = $\frac{6}{2}$ = 3 cm ⇒ AX = radius = 6 (The circles pass through each other’s centre) Now, in $\triangle XAO$ right angled at O ⇒ AX 2 = AO 2 + XO 2 ⇒ 6 2 = AO 2 + 3 2 ⇒ AO 2 = 36 – 9 ⇒ AO 2 = 27 ⇒ AO = $3\sqrt{3}\ \text{cm}$ $\therefore$ AB = 2 × AO = $6\sqrt{3}\ \text{cm}$ Hence, the correct answer is $6\sqrt3\ \text{cm}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : Two circles having equal radii intersect each other such that each passes through the centre of the other. The length of the common chord is 24 cm, so what will be the diameter of each circle?
Question : Two circles having equal radii intersect each other such that each passes through the centre of the other. The sum of the diameter of these two circles is 84 cm. What is the length of the common chord?
Question : Two circles having radii of $r$ units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is:
Question : Two circles of radii 15 and 18 cm touch each other externally. What is the length (in cm) of the direct common tangent to the two circles?
Question : Two circles touch each other internally. Their radii are 3 cm and 4 cm. What is the length of the biggest chord of the circle with radii of 4 cm which is outside the inner circle?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile