MathDB

7

Part of 2021 Novosibirsk Oral Olympiad in Geometry

Problems(2)

area by 2 congrurent rectangles (2021 Novosibirsk Oral Geo Oly 7.7)

Source:

4/27/2021
Two congruent rectangles are located as shown in the figure. Find the area of the shaded part. https://cdn.artofproblemsolving.com/attachments/2/e/10b164535ab5b3a3b98ce1a0b84892cd11d76f.png
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A_1B_1//<B bisector, circle with center I (2021 Novosibirsk Oral Geo Oly 9.7)

Source:

5/25/2021
A circle concentric with the inscribed circle of ABCABC intersects the sides of the triangle at six points forming a convex hexagon A1A2B1B2C1C2A_1A_2B_1B_2C_1C_2 (points C1C_1 and C2C_2 on the ABAB side, A1A_1 and A2A_2 on BCBC, B1B_1 and B2B_2 on ACAC). Prove that if line A1B1A_1B_1 is parallel to the bisector of angle BB, then line A2C2A_2C_2 is parallel to the bisector of angle CC.
parallelincentergeometry