NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 52 of 100

Marks: +1, -0

A circle is inscribed in a right angled triangle of perimeter 771. Then the ratio of numerical values of circumference of the circle to the area of the right angled triangle is

$4:7$
$3:7$
$2:7$
$1:7$

Validate

Solution:

Area of Δ ABC= [ar(Δ AOB) + ax(Δ BOC) + ax(Δ AOC)

=\;\;{1}/{2}AB×r+\;\;{1}/{2}×BC×r+AC×r

=\;\;{1}/{2}r[AB+BC+AC]

=\;\;{1}/{2}r×7π

∴\;\;{\;\text"Circumference of circle"\;}/{\;\text"Area of triangle"\;}=\;\;{2πr}/{\;\;{1}/{2}r×7π}={4}/{7}

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