The midpoints of the sides BC, CA and AB of a `triangle ABC` are D(2,1), E(-5,7)and F-5, -5) respectively. Find the equations of the sides of `triangle ABC`.
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In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then fin
Let the side equilateral triangleABC be a Area of triangle, `Delta = (a xx 4 + a xx 5 + a xx 6)/(2)` or `(a (4 + 5 + 6))/(2)...
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Each side of triangle ABC is divided into three equal parts. Find the ratio of the are of hexagon `P Q R S T U` to the area of the triangle ABC.
Area of hexagon PQRSTU `Delta_(1) = " area of " Delta ABC - " area of " Delta APQ - " area of " Delta BTU - " area of...
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In triangle ABC, `R (b + c) = a sqrt(bc)`, where R is the circumradius of the triangle. Then the triangle is
Correct Answer - C `R(b +c) = a sqrt(bc) = 2R sin A sqrt(bc)` `:. sin A = (b +c)/(2sqrt(bc))` Now `sin A le 1` `rArr (b + c)/(2sqrt(bc)) le 1`...
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If `R_(1)` is the circumradius of the pedal triangle of a given triangle ABC, and `R_(2)` is the circumradius of the pedal triangle of the pedal trian
Correct Answer - B Circumradius of triangle ABC, R = 5 `:.` Circumradius of pedal triangle, `R_(1) = 5//2` and so on. Now, `underset(i=1)overset(oo)sum R_(i) + R_(1) + R_(2) + R_(3)...
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In a triangle `ABC`, if `a,b,c` are the sides opposite to angles `A`, `B`, `C` respectively, then the value of `|{:(bcosC,a,c cosB),(c cosA,b,acosC),(
Correct Answer - C `(c )` `|{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}|` Apply `C_(1)toC_(1)+C_(3)` and using projection rule. `D=|{:(bcosC,a,c cosB+bcosC),(c cosA,b,acosC+c cosA),(acosB,c,bcosA+acosB):}|` `=|{:(bcosC,a,a),(c cosA,b,b),(acosB,c,c):}|=0`
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One side of an equilateral triangle is 36 cm. The mid-points of its sides are joined to form another triangle. Again another triangle is formed by joi
Correct Answer - `432sqrt3 cm^(2)`
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The midpoints of the sides BC, CA and AB of a `Delta ABC` are D(3, 4), E(8, 9) and F(6, 7) respectively. Find the coordinates of the vertices of the t
Correct Answer - A(11, 12), B(1, 2), C(5, 8)
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Find the area of `Delta ABC` with vertices A(0, -1), B(2, 1) and C(0, 3). Also, find the area of the triangle formed by joining the midpoints of its s
Correct Answer - 4 sq units, 1 sq unit
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ABC is an equilateral triangle with side 10 cm. The perimeter of the triangle formed by joining the mid points of the sides of ΔABC is
Correct option is C) 15 cm
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