$△$ ABC is a right angled triangle, right angled at B. BD is perpendicular as shown. What is $A C \times D C$ ?

BC.AB

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${B C}^{2}$

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${B D}^{2}$

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AB.AC

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Solution

The correct option is B
${B C}^{2}$

Consider $Δ$ ABC and $Δ$ BDC,

$∠$ ABC = $∠$ BDC = $90^{\circ}$

$∠$ C = $∠$ C [Common angle]

Therefore by AA similarity criterion, $△$ ABC and $△$ BDC are similar.

$\frac{A C}{B C}$ = $\frac{B C}{D C}$

$B C^{2}$ = $A C \times D C$

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