Question

In the figure, AB = BC and AD is perpendicular to CD. Then, \(AC^2=\)

• A. SAS
• B. SSS
• C. ASA
• D. None of these

Answer 1

The correct option is D

None of these

In $\Delta ADC$, using Pythagoras theorem,

$A{C}^2=A{D}^2+D{C}^2$

$A{D}^2=A{B}^2-B{D}^2\left(\text{In}\Delta ADB\right)$

$D{C}^2=(DB+BC{)}^2$

Putting values,

$A{C}^2=(A{B}^2-B{D}^2)+(D{B}^2+B{C}^2+2DB.BC)$

$=A{B}^2+B{C}^2+2DB.BC$

Since AB = BC,

$A{C}^2=2B{C}^2+2DB.BC$

$=2BC(BC+DB)$

$A{C}^2=2BC.DC$