Geometry – Concept testers

For each of the statements given below, say true or false

1. Any two triangles that are congruent to each other will also be similar to each other
2. If in a triangle with sides a, b and c, if a^2 + b^2 > c^2 the triangle has to be acute-angled
3. Any parallelogram inscribed inside a circle has to be a rectangle
4. If in a triangle the orthocenter, incenter and circumcenter are collinear the triangle has to be isosceles.
5. There will be a unique circle passing through any three points
6. If two circles with centers A and B and radii r and R intersect, then AB > R – r
7. Circumradius of a triangle cannot be greater than the three sides of the triangle
8. For any obtuse-angled triangle, the orthocenter and circumcenter will lie outside the triangle
9. In a scalene triangle, the sum of the three medians will be greater than the sum of the three altitudes.
10. In circumcircle and incircle are concentric, the triangle has to be equilateral

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