It's a circle

Geometry Level 3

In the figure shown, two identical circles of radius 12 cm each are drawn with centres C and C' with AB and BD being their respective tangents at A and D.If BE is their common tangent and AB perpendicular to BD, then find the length of BD.


The answer is 28.97056.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Siva Prasad
Nov 23, 2015

Look The figure

Triangle OHO' is right angled with angles 45, 45 and 90

So ratio of sides is 1 : 1 : 2 1:1: \sqrt{2}

The length of line OO' = radius of the circle × \times 2

So OO' = 12 × 2 \times 2 = 24

Then OH = O'H = 24 2 \frac { 24 }{ \sqrt { 2 } }

If the point where two lines join is considered as M Then CHBM is a square

So MB = BH

BH = 24 2 + 12 \frac { 24 }{ \sqrt { 2 } } +12 = 28.970 \boxed{28.970}

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