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Qn #1737
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Qn #1619
Let $\vec{a}, \vec{b}, \vec{c}$ be the position vectors of three vertices A, B, C of a triangle respectively then the area of this triangle is given by
Qn #1610
The equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, –1). The length of the side of the triangle is.
Qn #1603
Qn #1581
Let $\Delta ABC$ be a triangle whose area is $10\sqrt{3}$ units with side lengths $|AB|= 8$ units and $|AC|=5$
units. Find possible values of the angle A
Qn #1563
Qn #1561
The median AD of ΔABC is bisected at E and BE is produced to meet the side AC at F. Then, AF ∶ FC is
Qn #1548
If A, B and C is three angles of a ΔABC, whose area is Δ. Let a, b and c be the sides opposite to the
angles A, B and C respectively. Is $s=\frac{a+b+c}{2}=6$, then the product $\frac{1}{3} s^{2} (s-a)(s-b)(s-c)$ is equal to
Qn #1518
An equilateral triangle is inscribed in the parabola $y^{2} = 4ax$, such that one of the vertices of the triangle
coincides with the vertex of the parabola. The length of the side of the triangle is:
Qn #1447
If the angles of a triangle are in the ratio 2 : 3 : 7, then the ratio of the sides opposite to these
angles is
Qn #1445
In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is
Qn #1424
If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then
equation of the line BC is
Qn #1271
Qn #1256
In a triangle ABC, let angle C = π/2. If R is the inradius and R is circumradius of the triangle ABC,
then 2(r + R) equals
Qn #1243
If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in
Qn #1196
Qn #1173
The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0, (1+p)(x-q)+q(1+ q)=0 and y=0 where p≠q is
Qn #1169
Qn #1099
Qn #1058
The median AD of ΔABC is bisected at E and BE is extended to meet the side AC in F. The AF : FC =
Qn #1057
In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =
Qn #1028
Vertices of the vectors i - 2j + 2k , 2i + j - k and 3i - j + 2k form a triangle. This triangle is
Qn #855
The lines $px+qy=1$ and $qx+py=1$ are respectively the sides AB, AC of the triangle ABC and the base BC is bisected at $(p,q)$. Equation of the median of the triangle through the vertex A is
Qn #851
In a triangle ABC, $a\cos ^2\frac{C}{2}+\, c\, \, {\cos }^2\frac{A}{2}=\frac{3b}{2}$ then the sides of the triangle are in
Qn #847
In a triangle, if the sum of two sides is x and their product is y such that (x+z)(x-z)=y, where z is the third side of the triangle , then triangle is
Qn #837
If the position vector of A and B relative to O be $\widehat{i}\, -4\widehat{j}+3\widehat{k}$ and $-\widehat{i}\, +2\widehat{j}-\widehat{k}$ respectively, then the median through O of ΔABC is:
Qn #831
In a ΔABC, if $\tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k$ , then k is always