×

# Xuming's Synthetic Geometry Group- Mehul's Proposal

Q1)Let ABC be a triangle in which ∠A = $$60^ {\circ}$$ Let BE and CF be the bisectors of the angles ∠B and ∠C with E on AC and F on AB. Let M be the reflection of A in the line EF. Prove that M lies on BC.

Q2) Let ABCD be a convex quadrilateral. Let E, F, G, H be midpoints of AB, BC, CD, DA respectively. If AC, BD, EG, FH concur at a point O, prove that ABCD is a parallelogram.

Q3) (Extra one) Let ABC be an acute angled scalene triangle with circumcenter O and orthocenter H. If M is the midpoint of BC, then show that AO and HM intersect at the circumcircle of ABC.

(Problems taken from previous year RMO papers)

Note by Mehul Arora
2 years, 4 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

- 2 years, 4 months ago

@Calvin Lin @Xuming Liang Hope you like these! :)

- 2 years, 4 months ago