AP ICET 2016 Paper

Question : 114 of 200

Marks: +1, -0

A, B are end points of the longest chord of a circle of radius 3 units. If O is the centre of the circle and C is a point on the circle such that AC = >VO, then the perimeter of the triangle ABC is

$9+3-√3$
$9√3$
$6+3√3$
$3+6√3$

Validate

Solution:

Since A and B are end points of the longest chord of the circle,
AB is its
diameter. Hence ∠ACB = 900 as angle inscribed in a semicircle is a right angle.
Thus we have Δ ABC right angled at C.
Given, AC = AO = 3 cm

⇒BC=√{AB^2-AC^2}=√{6^2-3^2}=√27

⇒BC=3√3

units
∴ Perimeter of Δ ABC

=AB+BC+AC

=6+3√3+3=9+3√3

units

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