Mathematics - Circle Question with Solution | TestHub

MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q66-68: ABCD is a rectangle with AB = a > 0 and BC = b > 0. A circle through A, B touches CD and has radius r1; another circle through B, C touches AD and has radius r2.

$A BC D$ is a rectangle with $A B = a > 0, BC = b > 0$ . A circle through $A, B$ touches $C D$ and has radius $r_{1}$ . Another circle through $B, C$ touches $A D$ and has radius $r_{2}$ . Find $r_{1}$ .

Options:

Answer:

Solution:

The centre lies on the perpendicular bisector of $A B$ . If it is $h$ above $A B$ , then $r_{1}^{2} = h^{2} + (a /2)^{2} = (b - h)^{2}$ , giving $r_{1} = (4 b^{2} + a^{2}) / (8 b)$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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