This is a solution to a problem from American Mathematics Competition (AMC) 8 2020 Problem 18 based on Geometry.

AMC 8 2018 Problem 24

In the cube $ABCDEFGH$ with opposite vertices $C$ and $E,$ $J$ and $I$ are the midpoints of edges $\overline{FB}$ and $\overline{HD},$ respectively. Let $R$ be the ratio of the area of the cross-section $EJCI$ to the area of one of the faces of the cube. What is $R^2?$

(A) $\frac{5}{4}$ (B) $ \frac{4}{3} $ (C) $ \frac{3}{2} $ (D) $ \frac{25}{16}$  (E)  $\frac{9}{4}$.

Solution:

Useful Resources

• Year-wise Geometry Problems from AMC 8
• AMC 8 - Problem 18 (2020) - Learn to Apply Pythagoras Theorem
• AMC Program at Cheenta

This is a solution to a problem from American Mathematics Competition (AMC) 8 2020 Problem 18 based on Geometry.

AMC 8 2020 Problem 18

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 $A B C D ?$

(A) $240$ (B) $248$ (C) $256$ (D) $264$ (E) $272$.

Solution:

Useful Resources

• Year-wise Geometry Problems from AMC 8
• AMC 8 - Solid Geometry - 2018 Problem 24
• AMC Program at Cheenta