ICSE Class 10 Answered

Two circles with radii r cm and 7 cm have their centres 15 cm apart. If the length of the transverse common tangent is 9 cm, find r.

Asked by Topperlearning User | 06 Oct, 2017, 01:26: PM

Expert Answer

Length of transverse common tangent = $square root of straight d squared minus left parenthesis straight r subscript 1 plus straight r subscript 2 right parenthesis squared end root$

Here, d = 15 cm, r₁ = r cm, r₂ = 7 cm and length of transverse common tangent = 9 cm

Thus, we have

$9 squared equals 15 squared minus left parenthesis straight r plus 7 right parenthesis squared rightwards double arrow left parenthesis straight r plus 7 right parenthesis squared equals 15 squared minus 9 squared equals 144 rightwards double arrow straight r plus 7 equals 12 space.... left parenthesis straight r plus 7 equals minus 12 space is space not space possible right parenthesis rightwards double arrow straight r equals 5 space cm$