Question : If the distance between the centres of two circles is 12 cm and the radii are 5 cm and 4 cm, then the length (in cm) of the transverse common tangent is:
Option 1: $9$
Option 2: $\sqrt{143}$
Option 3: $\sqrt{63}$
Option 4: $7$
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: $\sqrt{63}$
Solution : Given, the distance between the centres of two circles is 12 cm ($d$) and the radii are 5 cm ($r_1$) and 4 cm ($r_2$). Length of the transverse common tangent line to the circle = $\sqrt{d^2-(r_1+r_2)^2}$ = $\sqrt{12^2-(5+4)^2}$ = $\sqrt{144-81}$ = $\sqrt{63}\ \text{cm}$ Hence, the correct answer is $\sqrt{63}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : 8 cm and 5 cm are the radii of two circles. If the distance between the centres of the two circles is 11 cm, then the length (in cm) of the common tangent of the two circles is:
Question : If the radii of two circles are 7 cm and 4 cm and the length of the transverse common tangent is 13 cm, then the distance between the two centres is:
Question : The distance between the centres of two circles having radii of 24 cm and 18 cm, respectively, is 48 cm. Find the length (in cm) of a direct common tangent to the two circles.
Question : The distance between the centres of two circles of radii 6 cm and 3 cm is 15 cm. The length of the transverse common tangent to the circles is:
Question : Two circles of radius 2.4 cm and 4 cm, respectively, have a common tangent. The distance between the centres of the two circles is 6.5 cm. If the common tangent does not intersect the line joining the centres, then find the length of a common tangent to the circles.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile