Two circles C1 and C2 touch each other externally and the line ''l'' is a common tangent The line - Maths - Circles

Question

Two circles C1 and C2 touch each other
externally and the line ''l'' is a common tangent The line m is
parallel to l and touches the two circles C1 and
C3 The three circles mutually touch each other The
radius of C2 is 9 And the radius of C​3
is 4 Find the radius of C1

Anuradha Sharma · Accepted Answer

Hi, The figure can be drawn as, P, R and T are the centers of the circles PQ and ST are parallel to the common tangent lines m and l

Including some dimensions I let r be the radius of C1

Since PQ and ST are parallel to the tangent lines. PQR and RST are right triangles and hence Pythagoras' Theorem can be used to find the lengths of PQ ans ST. Now draw a line trough T, parallel to SQ and meeting PQ at W.

PWT is a right triangle and hence Pythagoras' Theorem applied to this triangle gives a quadratic you can solve for r Regards

Two circles C1 and C2 touch each other externally and the line ''l'' is a common tangent. The line m is parallel to l and touches the two circles C1 and C3. The three circles mutually touch each other. The radius of C2 is 9. And the radius of C​3 is 4. Find the radius of C1.

Two circles C₁ and C₂ touch each other externally and the line ''l'' is a common tangent. The line m is parallel to l and touches the two circles C₁ and C₃. The three circles mutually touch each other. The radius of C₂ is 9. And the radius of C₃ is 4. Find the radius of C_1.