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State true or false. (a) The altitude ...

State true or false.
(a) The altitude of an acute-angled triangle lies outside the triangle.
(b) the orthocentre of an obtuse-angled triangle lies outside the triangle.
(c) the orthocentre is the point of concurrency of three medians of a triangle.
(d) The vertex containing the right angle is also the orthocentre of a right-angled triangle.

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If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a^2+1,a^2+1) and (2a ,-2a), then find the orthocentre.

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ICSE-THE TRIANGLE AND ITS PROPERTIES-TRY THIS
  1. State true or false. (a) A median of a triangle may lie outside the ...

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  2. Draw a rought sketch of a right-angled triangle. Draw all the three al...

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  3. State true or false. (a) The altitude of an acute-angled triangle li...

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  4. Find the value of x in the figure.

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  5. One exterior angle of a triangle is 70^(@). The two opposite interior ...

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  6. In the given figure, find x and y.

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  7. Find the third angle of a triangle, two of whose angles are 65^(@) and...

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  8. One angle of a triangle is thrice the smallest angle and the other ang...

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  9. In DeltaABC,angleB=90^(@) and AE and CF are the angle bisector (line s...

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  10. Find angleA+angleB+angleC+angleD

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  11. Find the values of x,y, and z in the following figure.

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  12. Find the length of AB in each of the following

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  13. Find the value of x in each of the following triangles.

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  14. Find the values of x and y.

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  15. If one of the base angles of an isosceles triangle measures 30^(@), fi...

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  16. Can the lengths 5 cm, 9 cm, andd 13 cm be the dimensions of a triangle...

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  17. Two sides of an isosceles triangle are 4 cm and 7. what is the possibl...

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  18. A point O lies inside a DeltaABC. Show that OA+OB+OC gt (1)/(2)(AB+BC+...

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  19. Find the value of x in each of the following figures.

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  20. A ladder is placed with one edge on the wall 15 feet above the ground ...

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