JEE Class main Answered
three circles
Asked by vaibhavsinghsirsaganj | 15 Mar, 2024, 04:35: PM
Expert Answer
Let A is centre of small circle of radius 3 cm . Let B is centre of circle of radius 6 cm .
Let C be the centre of circle that just encloses the circles of radii 3cm and 6 cm as shown in figure.
Common tangent KL make contact with circles at D and E.
Hence if we draw lines AD and BE , these lines are perpendicular to KL.
Let us draw a perpendicular line CF from C to KL.
In ΔXBE, we have AD | | BE . Hence we have
From above expression, we get , XA = AB = 9 cm
In ΔXCF, we have AD | | CF . Hence we have
Hence we get , CF = (5/3) AD = (5/3) × 3 = 5 cm
Since CF is perpendicular to the chord KL , we get
KL = 2 KF = 15 cm
Answered by Thiyagarajan K | 16 Mar, 2024, 05:13: PM
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