query: Finding the radius of incircle of $\triangle ABC$ where each of three other circles is mutually tangent to two sides of the triangle respectively
positive_passages.docid: 148147
positive_passages.text: Three circles having centres on the three sides of a triangle
negative_passages.docid: 79777
negative_passages.text: An olympiad Geometry problem involving triangles
negative_passages.docid: 94091
negative_passages.text: In $ \triangle ABC$ show that $ 1 \lt \cos A + \cos B + \cos C \le \frac 32$
negative_passages.docid: 89493
negative_passages.text: Prove that circumcentre of $ABH,BCH,CAH$ are the vertices of a triangle congruent to $ABC$
negative_passages.docid: 131526
negative_passages.text: Prove that the Tangent of 75 degrees equals 2 plus the square-root of 3
negative_passages.docid: 81777
negative_passages.text: Sum of radii of intersecting circles internally tangent to another circle
negative_passages.docid: 148963
negative_passages.text: The Ellipse Problem - finding an ellipse inside a triangle
negative_passages.docid: 106141
negative_passages.text: Find the area ratio between ABC and the hatched triangle.
negative_passages.docid: 111292
negative_passages.text: Find all triangles of which perimeter and area are numerically equal
negative_passages.docid: 216
negative_passages.text: In a $\triangle ABC,a^2+b^2+c^2=ac+ab\sqrt3$,then the triangle is
negative_passages.docid: 127866
negative_passages.text: Two triangles and their content ratio
negative_passages.docid: 43398
negative_passages.text: Find possible number of triangles with integer sides for a given inradius
negative_passages.docid: 130470
negative_passages.text: Find the angle ADE of the given triangle.
negative_passages.docid: 61343
negative_passages.text: Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
negative_passages.docid: 79364
negative_passages.text: Finding the circles passing through two points and touching a circle
negative_passages.docid: 149319
negative_passages.text: Möbius transformations and concentric circles
negative_passages.docid: 56320
negative_passages.text: Prove that the circumradius of $\triangle PAB$ is constant