MathDB

1

Part of 2022 Malaysia IMONST 2

Problems(3)

IMONST2 Senior 2022 #1

Source: IMONST2 Senior 2022 #1

9/15/2022
Given a circle Γ\Gamma with center II, and a triangle △ABC\triangle ABC with all its sides tangent to Γ\Gamma. A line ℓ\ell is drawn such that it bisects both the area and the perimeter of △ABC\triangle ABC.
Prove that line ℓ\ell passes through II.
geometryincentertangent
IMONST2 2022 Junior #1

Source: IMONST2 2022 Junior #1

9/17/2022
Given a circle and a quadrilateral ABCDABCD whose vertices all lie on the circle. Let RR be the midpoint of arc ABAB. The line RCRC meets line ABAB at point SS, and the line RDRD meets line ABAB at point TT.
Prove that CDTSCDTS is a cyclic quadrilateral.
geometrycyclic quadrilateral
[IMONST2 2022 Primary #1] Number of diagonals

Source:

7/4/2023
Given a polygon ABCDEFGHIJABCDEFGHIJ. How many diagonals does the polygon have?
geometry