Question

If $p,q,r$ be lengths of perpendiculars from vertices of triangle $ABC$ on any line, prove $a^2(p-q)(p-r)+b^2(q-r)(q-p)+c^2(r-p)(r-q)=4\Delta^2$

score 571 · Answer 1 · 2018-11-21 07:56:26

571

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If $p,q,r$ be lengths of perpendiculars from vertices of triangle $ABC$ on any line, prove $a^2(p-q)(p-r)+b^2(q-r)(q-p)+c^2(r-p)(r-q)=4\Delta^2$

Published on 21 Nov 2018 - 7:56

score 2k · Answer 2 · 2018-11-21 18:22:37

2k

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An equilateral triangle is inscribed in a circle of radius $r$. If $P$ is any point on the circumference, find the value of $PA^2 + PB^2 + PC^2$.

Published on 21 Nov 2018 - 18:22

score 7k · Answer 3 · 2018-11-22 11:29:15

7k

Views

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score 206 · Answer 4 · 2026-03-25 14:22:31

206

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46

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score 69 · Answer 6 · 2018-11-25 09:52:20

For pair of st. lines , length of line joining feet of perpendiculars from $(f,g)$ to them is$\sqrt {4.\frac {(h^2-ab)(f^2+g^2)}{(a-b)^2+4h^2}}$

score 52 · Answer 7 · 2018-11-26 10:45:29

52

Views

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Published on 26 Nov 2018 - 10:45

score 77 · Answer 8 · 2018-11-27 13:59:56

77

Views

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score 22 · Answer 9 · 2026-03-25 23:16:18

22

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score 106 · Answer 11 · 2018-11-28 12:57:10

106

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71

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102

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score 6.4k · Answer 14 · 2026-03-26 07:58:43

6.4k

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score 427 · Answer 15 · 2026-03-25 10:52:29

427

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List Question

If $p,q,r$ be lengths of perpendiculars from vertices of triangle $ABC$ on any line, prove $a^2(p-q)(p-r)+b^2(q-r)(q-p)+c^2(r-p)(r-q)=4\Delta^2$

An equilateral triangle is inscribed in a circle of radius $r$. If $P$ is any point on the circumference, find the value of $PA^2 + PB^2 + PC^2$.

Finding the intersection points of a line with a cube

Parametrization of distance to non-unit circle/sphere with non-centered origin

How to show that the bipolar co-ordinates are othogonal

For pair of st. lines , length of line joining feet of perpendiculars from $(f,g)$ to them is$\sqrt {4.\frac {(h^2-ab)(f^2+g^2)}{(a-b)^2+4h^2}}$

Equation of line: find $p + q$

Prove that locus of vertex is $(a+b)(x^2+y^2)+2h(x\beta + \alpha y) + (a-b)(x\alpha - y\beta)=0$

Optimum mapping between tesselated parallelograms and tesselated rectangles?

Can all quadric surfaces be obtained by cutting a 4-dimensional cone?

Unit circle shifted upwards so it is tangent the graph of $f(x)=x^{2}$

constructing a spiral

Co-ordinate Geometry : Circle

How to convert a straight line into polar coordinates?

Finding coordinate in a quadrilateral

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