GATE 2026 MA – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Three externally tangent circles C₁,C₂,C₃ have centers O₁,O₂,O₃ and radii r₁ = 2 cm, r₂ = 1 cm, r₃. The shown angle O₁O₃O₂ is 90°. Find r₃ in cm.

$(-3+\sqrt{17})/2$
$(3+\sqrt{17})/2$
$(-2+\sqrt{17})/2$
$(-3+2\sqrt{17})/2$

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Show answer and explanation

Correct answer: (A) $(-3+\sqrt{17})/2$

Explanation

Center distances are 2+r₃, 1+r₃ and 3. The right triangle gives $(2+r_3)^2+(1+r_3)^2=3^2$. Simplify to r₃²+3r₃−2 = 0. The positive root is **(−3+√17)/2, A**.

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