There are two circles C1 and C2 whose radii are r1,r2 , respectively. If distance between their centre is 3r1-r2 and length of direct common tangent is twice of the length of transverse common tangent. Then r1:r2 is

Question

There are two circles C1 and C2 whose radii are r1,r2 , respectively. If distance between their centre is 3r1-r2 and length of direct common tangent is twice of the length of transverse common tangent. Then r1:r2 is (A) 5:4 (B) 6:5 (C) 7:6 (D) 8:7

Tardigrade Admin · Accepted Answer

Length of direct common tangent =√d2 - (r1 - r2)2 Length of transverse common tangent =√d2 - (r1 + r2)2 Where d is distance between their centre. Then (√d2 - (r1 - r2)2)=2(√d2 - (r1 + r2)2) d2=(r12 + r22 + (10/3) r1 r2), where d=3r1-r2 (3 r1 - r2)2=r12+r22+(10/3)r1r2 r1:r2=7:6

Q. There are two circles $C_{1}$ and $C_{2}$ whose radii are $r_{1}, r_{2}$ , respectively. If distance between their centre is $3 r_{1} - r_{2}$ and length of direct common tangent is twice of the length of transverse common tangent. Then $r_{1} : r_{2}$ is

$5 : 4$

$6 : 5$

$7 : 6$

$8 : 7$

Q. There are two circles C1​ and C2​ whose radii are r1​,r2​ , respectively. If distance between their centre is 3r1​−r2​ and length of direct common tangent is twice of the length of transverse common tangent. Then r1​:r2​ is

5:4

6:5

7:6

8:7

Q. There are two circles $C_{1}$ and $C_{2}$ whose radii are $r_{1}, r_{2}$ , respectively. If distance between their centre is $3 r_{1} - r_{2}$ and length of direct common tangent is twice of the length of transverse common tangent. Then $r_{1} : r_{2}$ is

$5 : 4$

$6 : 5$

$7 : 6$

$8 : 7$