Try this beautiful Problem based on area from AMC 8 2020.
Rectangle $A B C D$ is inscribed in a semicircle with diameter $\overline{F E}$, as shown in the figure. Let $D A=16$, and let $F D=A E=9$. What is the area of $A B C D$ ?
Area
Semi circle
Symmetry
AMC 8 2020 Problem 13
240
Try to find the diameter of the semicircle. So the diameter will be,
The diameter of the semicircle is $9+16+9=34$, so $O C=17$. By symmetry, $O$ is the midpoint of AD,So, $AO=OD=\frac{16}{2}=8$.
Now, apply Pythagorean Theorem to find CD,
SO the area of ABCD will be=$AD \times CD$
Try this beautiful Problem based on area from AMC 8 2020.
Rectangle $A B C D$ is inscribed in a semicircle with diameter $\overline{F E}$, as shown in the figure. Let $D A=16$, and let $F D=A E=9$. What is the area of $A B C D$ ?
Area
Semi circle
Symmetry
AMC 8 2020 Problem 13
240
Try to find the diameter of the semicircle. So the diameter will be,
The diameter of the semicircle is $9+16+9=34$, so $O C=17$. By symmetry, $O$ is the midpoint of AD,So, $AO=OD=\frac{16}{2}=8$.
Now, apply Pythagorean Theorem to find CD,
SO the area of ABCD will be=$AD \times CD$
