Search found 155 matches

Sun Nov 22, 2015 1:18 am
Forum: Secondary Level
Topic: geometry
Replies: 3
Views: 1249

Re: geometry

$BD$ will be a tangent $\Leftrightarrow OB\perp BD \Leftrightarrow OB||AC \Leftrightarrow \angle ABO=\angle BAC \Leftrightarrow \angle BAO=\angle BAC$
Wed May 20, 2015 12:51 am
Forum: Geometry
Topic: Geometric Inequality
Replies: 1
Views: 698

Re: Geometric Inequality

Any hints? I'm stuck... Mon May 04, 2015 8:39 pm
Forum: Geometry
Replies: 5
Views: 1252

Extremely sorry for the typo... Sun May 03, 2015 2:35 pm
Forum: Geometry
Replies: 5
Views: 1252

The quadrilateral $ABCD$ is excribed around a circle with centre $I$. Prove that, the projections of $B$ and $D$ on $IA$, $IC$ lie on a circle.

Sharygin Geometry Olympiad, Russia
Sun May 03, 2015 1:43 am
Forum: Geometry
Topic: triangular inequality [sides and area]
Replies: 3
Views: 946

Re: triangular inequality [sides and area]

This was also set as Problem No. 2 in the 1961 IMO. Wed Apr 29, 2015 9:39 pm
Forum: Algebra
Topic: Inequality (sin, r and s)
Replies: 2
Views: 916

Inequality (sin, r and s)

Prove the inequality,
$\frac{1}{\sqrt{2\sin A}}+\frac{1}{\sqrt{2\sin B}}+\frac{1}{\sqrt{2\sin C}}\leq \sqrt{\frac{s}{r}}$
where, $s$ and $r$ are the semi-perimeter and inradius of $\triangle ABC$.

Sharygin Geometry Olympiad, Russia
Mon Apr 27, 2015 7:41 pm
Forum: Geometry
Topic: cool geo
Replies: 4
Views: 1111

Re: cool geo

Corrected. Sun Apr 26, 2015 10:31 pm
Forum: Geometry
Topic: cool geo
Replies: 4
Views: 1111