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 triangle.
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In triangle ABC, `sinA sin B + sin B sin C + sin C sin A = 9//4 and a = 2`, then the value of `sqrt3 Delta`, where `Delta` is the area of triangle, is
Correct Answer - 3 The given equation is `4 sin A sin B + 4 sin B sin C + 4 sin C sin A = 9` `rArr 2 cos (A...
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Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C, respectivelu. Suppose `a = 6, b = 10` and
Correct Answer - 3 `Delta = (1)/(2) ab sin C rArr sin C = (2Delta)/(ab) = (2 xx 15 sqrt3)/(6 xx 10) = (sqrt3)/(2)` `rArr C = 120^(@)` `rArr c =...
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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 `triangl
Correct Answer - x-2=0, 6x-7y+79=0, 6x+7y+65=0
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Find the (i) lengths of major and minor axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity, and (v) length of th
Correct Answer - (i) 10 units, 8 units (ii) ` A(-5, 0) and B(5, 0) " "` (iii) `F_(1) (-3, 0) and F_(2) (3, 0) ` (iv) ` e= 3/5"...
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D and E are points on the sides AB and AC respectively of `Delta ABC `. In each of the following cases, determine whetheer `DE||BC` or not. (i) `AD=5.
Correct Answer - (i) Yes (ii) No (iii) Yes (iv) No
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The corresponding sides of two similar triangles ABC and DEF are `BC=9.1 cm, and EF=6.5cm`. If the perimete of `Delta DEF` is 25 cm, find the perimete
Correct Answer - 35 cm
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Two triangles ABC and PQR are such that `AB=3 cm, AC=6 cm, angle A=70^(@), PR=9 cm, angle P=70^(@) and PQ=4.5 cm`. Show that `Delta ABC~Delta PQR` and
Correct Answer - SAS-similarity
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Find the area of `Delta ABC` whose vertices are : (i) A(1, 2), B (-2, 3) and C(-3, -4) (ii) A(-5, 7), B(-4, -5) and C(4, 5) (iii) A(3, 8), B(-4, 2) an
Correct Answer - (i) 11 sq units (ii) 53sq units (iii) 37.5 sq units (iv) 24.5 sq units
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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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Using vectors, find the area of `Delta` ABC whose vertices are (i) A(1,1,2),B(2,3,5) and C(1,5,5) (ii) A(1,2,3),B(2,-1,4) and C(4,5,-1) (iii) A(3,-1,2
Correct Answer - (i) `1/2 sqrt(61)` sq units (ii) `1/2 sqrt(274)`sq units (iii)`1/2sqrt(165)` sq units (iv) `sqrt(13)` sq units
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