Question

Prove area of a quadrilateral is $\frac14[4m^2n^2-(b^2+d^2-a^2-c^2)^2]^{\frac12}$

score 102 · Answer 1 · 2015-08-17 17:52:43

102

Views

Prove area of a quadrilateral is $\frac14[4m^2n^2-(b^2+d^2-a^2-c^2)^2]^{\frac12}$

Published on 17 Aug 2015 - 17:52

score 2.1k · Answer 2 · 2015-08-18 09:15:07

2.1k

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Collinearity problem (Newton-Gauss line)

Published on 18 Aug 2015 - 9:15

score 138 · Answer 3 · 2015-08-18 10:38:49

138

Views

Quadrilateral's area problem

Published on 18 Aug 2015 - 10:38

score 191 · Answer 4 · 2026-03-26 23:11:02

191

Views

Area of quadrilateral: $S \leq \frac{(a+b)(c+d)}4 $

Published on 26 Mar 2026 - 23:11

score 210 · Answer 5 · 2015-08-21 07:38:19

210

Views

Geometry - Trapezium and its properties

Published on 21 Aug 2015 - 7:38

score 73 · Answer 6 · 2015-08-25 15:35:53

73

Views

If $AD=999$ and $PQ=200$, find the sum of the radii of those incircles.

Published on 25 Aug 2015 - 15:35

score 500 · Answer 7 · 2026-03-25 15:50:23

500

Views

Very special geometric shape - parallelogram (No name yet?)

Published on 25 Mar 2026 - 15:50

score 725 · Answer 8 · 2015-09-07 09:17:30

725

Views

$ABCD$ is a convex quadrilateral in which $AB^2+CD^2=BC^2+AD^2$. Prove by vectors that diagonals $AC$ and $BD$ are orthogonal to each other.

Published on 07 Sep 2015 - 9:17

score 66.5k · Answer 9 · 2015-09-30 07:57:58

66.5k

Views

Find the length of the diagonal of a parallelogram given sides and angle between side and diagonal

Published on 30 Sep 2015 - 7:57

score 354 · Answer 10 · 2015-10-02 11:21:03

354

Views

Quadrilaterals with adjacent sides equal

Published on 02 Oct 2015 - 11:21

score 143 · Answer 11 · 2015-10-04 01:36:42

143

Views

Find $\angle{FPC}$: impossible question?

Published on 04 Oct 2015 - 1:36

score 158 · Answer 12 · 2026-03-28 08:40:07

158

Views

Prove that in a cyclic quadrilateral $ABCP$ where two of its sides are equal the ratio $ {PA\over PB + PC}= {AC\over BC}$ is constant for any point P

Published on 28 Mar 2026 - 8:40

score 57 · Answer 13 · 2015-10-05 21:10:36

57

Views

Follow-up to Find $\angle{FPC}$: impossible question?

Published on 05 Oct 2015 - 21:10

score 1.5k · Answer 14 · 2015-10-15 16:03:11

1.5k

Views

To find ratio of Length and Breadth of a Rectangle

Published on 15 Oct 2015 - 16:03

score 180 · Answer 15 · 2026-03-28 17:12:21

180

Views

Cyclic quadrilateral

Published on 28 Mar 2026 - 17:12

List Question

Prove area of a quadrilateral is $\frac14[4m^2n^2-(b^2+d^2-a^2-c^2)^2]^{\frac12}$

Collinearity problem (Newton-Gauss line)

Quadrilateral's area problem

Area of quadrilateral: $S \leq \frac{(a+b)(c+d)}4 $

Geometry - Trapezium and its properties

If $AD=999$ and $PQ=200$, find the sum of the radii of those incircles.

Very special geometric shape - parallelogram (No name yet?)

$ABCD$ is a convex quadrilateral in which $AB^2+CD^2=BC^2+AD^2$. Prove by vectors that diagonals $AC$ and $BD$ are orthogonal to each other.

Find the length of the diagonal of a parallelogram given sides and angle between side and diagonal

Quadrilaterals with adjacent sides equal

Find $\angle{FPC}$: impossible question?

Prove that in a cyclic quadrilateral $ABCP$ where two of its sides are equal the ratio $ {PA\over PB + PC}= {AC\over BC}$ is constant for any point P

Follow-up to Find $\angle{FPC}$: impossible question?

To find ratio of Length and Breadth of a Rectangle

Cyclic quadrilateral

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