In a circle of radius 8 cm AB and AC are two chords such that AB AC 12 cm What is the length of chor...........

Quantitative Aptitude (CDS) Mensuration 2D

In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?

$2\sqrt{6}\: cm$

$3\sqrt{6}\: cm$

$3\sqrt{7}\: cm$

$6\sqrt{7}\: cm$

O is the center of circle

Here ABC forms an isosceles triangle as AB=AC=12cm

So AE (a perpendicular bisector) passes through O as OE also bisects chord BC at right angle AD = DB = 6

In triangle ADO AO2 = AD2 + DO2 OD = √64 – 36 = √28

Now using similarity AEB~ADO

AB/AO = EB/DO

12/8 = (BC/2)/ √28

BC=6√7

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