ABC is a triangle with B as right angle, AC = 5 cm and AB = 4 cm.… - Vidyadip

MCQ

$ABC$ is a triangle with $B$ as right angle, $AC = 5\ cm$ and $AB = 4\ cm$. A circle is drawn with $A$ as centre and $AC$ as radius. The length of the chord of this circle passing through $C$ and $B$ is:

A
$3\ cm.$
B
$4\ cm.$
C
$5\ cm.$
✓
$6\ cm.$

✓

Answer

Correct option: D.

$6\ cm.$

$A D$ and $A C$ are radii of same circle and $C D$ is a chord.
Consider $\triangle \mathrm{ABC}$,
$B C^2=(A C)^2-(A B)^2$
$=5^2-4^2=25-16=9$
$\Rightarrow B C=3 \mathrm{~cm}$
Chord $C D=2 \times B C=6 \mathrm{~cm}$

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