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Question

In a circle of radius 5 cm, AB and AC are two equal chords such that AB=AC=6. Find the length of the chord BC
318359.png

A
9.8 cm
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B
9.6 cm
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C
9.2 cm
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D
7.3 cm
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Solution

The correct option is B 9.6 cm
R.E.F image
Given circle of radius =5cm
OA=OB=OC=5cm
and AB=AC=6cm,BC=?
Consider Δ le OAB & Δ le OAC OC=OB Both triangle are congruent
OA is common
OAC=OAB
Draw perpendicular from center O to AB at D
In Δle OAB, ODB=ODB=90AD=DB=AB2=3cm
OA=OB as D bisector AB
Applying Pythagoras theorem in Δ le ODBOD2+DB2=OB2
OD=4cm
Area of Δ OAB=12bh=12×AB×OD=12×6cm×4=12cm2
Let 'E' be the point where OA meets BC
It can be observed that AEC=AEB=90, further E bisector BC
BE=EC=BC2
Area of Δ le OAB, considering OA as base (b) & BE at height (h)
12sqcm=12×OA×BE
BE=245cm
BC=2×BE=485=9.6cm

1162892_318359_ans_19103f97653a4296b39a0e45df80591d.jpg

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