Mathematics · Circles

JEE Main 2024 — 5 April, Shift 2 — Question 16

Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC . Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies :

Option A:
$r=1$
Option B:
$r^{2}-8 r+8=0$
Correct
Option C:
$2 r^{2}-4 r+1=0$
Option D:
$2 r^{2}-8 r+7=0$

Answer: B

Step-by-step solution

OF^{2} &= r^{2} \\ (2 - r^{2}) + (2 - r)^{2} &= r^{2} \\ r^{2} - 8r + 8 &= 0 \end{aligned}$$

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Exam: JEE Main 2024
Paper: 5 April, Shift 2
Subject: Mathematics
Chapter: Circles
Topic: Considering a Line or a Point wrt a Circle

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Step-by-step solution

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