Maths · Co-ordinate of the centroid, orthocentre and circumcentre of a triangle
In an equilateral triangle with sides Angle bisectors of meet at point Measures
In an equilateral triangle \( \Delta A B C \) with sides \( 5 \mathrm{cm} . \) Angle bisectors of \( \angle A, \angle B, \angle C \) meet at point \( 0 . \) Measures of OA approximately is
- A. 2.5
- B. 4
- C. 3 .2 \)
- D. 2.8
Step-by-step solution
In an equilateral triangle, the angle bisectors intersect at the centroid, which is also the circumcenter and incenter. The distance from a vertex to the centroid is 2/3 of the altitude. Altitude of side 5 cm = (√3/2)*5 = (5√3)/2 ≈ 4.330 cm. Thus OA = (2/3)*altitude = (2/3)*(5√3/2) = (5√3)/3 ≈ 2.887 cm. Among the options, 2.8 cm is the closest approximation.
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