Answer:
The length of the diagonal AC=20 cm.
Step-by-step explanation:
From ΔOBP and ΔABC, we have
[tex]\frac{OB}{AB}=\frac{BP}{BC}[/tex]( O and P are mid points)
∠B=∠B(Common)
Therefore, by SAS rule,
ΔOBP is similar toΔABC
Thus, [tex]\frac{OB}{AB}=\frac{OB}{2OB}=\frac{1}{2}[/tex]
⇒[tex]\frac{OP}{AC}=\frac{1}{2}[/tex]
⇒[tex]AC=2{\times}OP[/tex]
⇒[tex]AC=2{\times}10[/tex]
⇒[tex]AC=20 cm[/tex]
Thus, the length of the diagonal AC=20 cm.
