Mathematics - Circle Question with Solution | TestHub

MathematicsCircleCommon tangents to two circlesHard2 minPYQ_2019

MathematicsHardsingle choice

Three circles of radii $a, b, c, (a < b < c)$ touch each other externally. If they have $x -$ axis as a common tangent, then:

Options:

Answer:

Solution:

We have,
$L M = P N = \sqrt{{(a + b)}^{2} - {(b - a)}^{2}} = 2 \sqrt{a b}$

$N Q = M S = \sqrt{{(a + c)}^{2} - {(c - a)}^{2}} = 2 \sqrt{a c}$

$P Q = S T = \sqrt{{(b + c)}^{2} - {(c - b)}^{2}} = 2 \sqrt{b c}$

$∵$ $P Q = P N + N Q$

$\Rightarrow 2 \sqrt{b c} = 2 \sqrt{a b} + 2 \sqrt{a c}$

$\Rightarrow \frac{1}{\sqrt{a}} = \frac{1}{\sqrt{b}} + \frac{1}{\sqrt{c}}$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Common tangents to two circles

⏱ 2mℹ️ Source: PYQ_2019

Doubts & Discussion

Loading discussions...