Mathematics - Circle Question with Solution | TestHub

MathematicsCircleCommon tangents to two circlesMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q84-86: C1 and C2 are unit circles with centres P=(0,0) and Q=(1,0). The unit circle C3 passes through P and Q; its centre R lies above the x-axis at (1/2, √3/2).

$C_{1}, C_{2}$ are unit circles with centres $P = (0, 0)$ and $Q = (1, 0)$ . The unit circle $C_{3}$ passes through $P, Q$ and has centre $R$ above the $x$ -axis, so $R = (1/2, 3 /2)$ . Which common tangent to $C_{1}$ and $C_{3}$ does not intersect $C_{2}$ ?

Options:

Answer:

Solution:

Both $P$ and $R$ are at distance 1 from the line $3 x - y + 2 = 0$ , whereas $Q$ is more than 1 unit away. The other displayed tangent passes through or meets $C_{2}$ .

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

⏱ 2mℹ️ Source: QB

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