Question 32
The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of direct common tangent to the length of the transverse common tangent?
Solution
Given distance between the centers=10 cm
Length of transverse common tangent=$$\sqrt{d^{2}-(r1+r2)^{2}}$$
=$$\sqrt{10^{2}-(3+4)^{2}}$$
=$$\sqrt{100-49}$$
=$$\sqrt{51}$$
Length of direct common tangent=$$\sqrt{d^{2}-(r1-r2)^{2}}$$
=$$\sqrt{100-1}$$
=$$\sqrt{99}$$
Ratio=$$\sqrt{99}/\sqrt{51}$$
=$$\sqrt{33}/\sqrt{17}$$
Get AI Help
Create a FREE account and get:
- Free SSC Study Material - 18000 Questions
- 230+ SSC previous papers with solutions PDF
- 100+ SSC Online Tests for Free
