Geometry – Page 233

Question-81610

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 81610 by TawaTawa last updated on 14/Feb/20 Answered by MJS last updated on 14/Feb/20 $2 ⩽ x ⩽ 4$ $let x = t^{2} + 2 \Rightarrow 0 ⩽ t^{2} ⩽ 2$ $$\mathrm{3}{t}−\mathrm{12}\sqrt{\mathrm{2}−{t}^{\mathrm{2}} }+\mathrm{21}{t}^{\mathrm{2}} −\mathrm{40}+{t}\sqrt{\mathrm{2}−{t}^{\mathrm{2}}…

Let-ABCDE-be-an-equiangular-pentagon-whose-side-lengths-are-rational-numbers-Prove-that-the-pentagon-is-regular-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 16077 by Tinkutara last updated on 17/Jun/17 $Let A B C D E be an equiangular$ $pentagon whose side lengths are$ $rational numbers . Prove that the$ $pentagon is regular .$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Let-K-L-M-and-N-be-the-midpoints-of-the-sides-AB-BC-CD-and-DA-respectively-of-a-cyclic-quadrilateral-ABCD-Prove-that-the-orthocenters-of-the-triangles-AKN-BKL-CLM-and-DMN-are-the-vertices-of-

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Question Number 16074 by Tinkutara last updated on 17/Jun/17 $Let K, L, M and N be the midpoints of$ $the sides A B, B C, C D and D A,$ $respectively, of a cyclic quadrilateral$ $A B C D . Prove that the orthocenters$ $of the triangles A K N, B K L, C L M and$ $D M N are the vertices of a$ $parallelogram .$ Terms…

prove-that-equation-of-a-circle-passing-through-the-points-of-intersection-of-a-circle-S-0-and-a-line-L-0-can-be-taken-as-S-L-0-where-is-a-parameter-

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Question Number 147144 by gsk2684 last updated on 18/Jul/21 $p r o v e t h a t$ $e q u a t i o n o f a c i r c l e p a s s i n g t h r o u g h$ $t h e p o i n t s o f i n t e r s e c t i o n o f a c i r c l e$ $S = 0 a n d a l i n e L = 0 c a n b e t a k e n a s$ $S + λ L = 0 w h e r e λ i s a p a r a m e t e r$ Answered by mr W last…

Prove-that-the-perpendiculars-dropped-from-the-midpoints-of-the-sides-of-a-cyclic-quadrilateral-to-the-opposite-sides-are-concurrent-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 16075 by Tinkutara last updated on 17/Jun/17 $Prove that the perpendiculars$ $dropped from the midpoints of the sides$ $of a cyclic quadrilateral to the opposite$ $sides are concurrent .$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Let-A-B-and-C-be-points-on-the-sides-BC-CA-and-AB-of-the-triangle-ABC-Prove-that-the-circumcircles-of-the-triangles-AB-C-BA-C-and-CA-B-have-a-common-point-Prove-that-the-property-holds-even

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Question Number 16071 by Tinkutara last updated on 21/Jun/17 $Let A^{'}, B^{'} and C^{'} be points on the sides$ $B C, C A and A B of the triangle A B C .$ $Prove that the circumcircles of the$ $triangles {A B}^{'} C^{'}, {B A}^{'} C^{'} and {C A}^{'} B^{'}$ $have a common point . Prove that the$ $property holds even if the points A^{'},$ $B^{'} and C^{'} are collinear .$ Answered…

Let-ABCD-be-a-convex-quadrilateral-Prove-that-the-orthocenters-of-the-triangles-ABC-BCD-CDA-and-DAB-are-the-vertices-of-a-quadrilateral-congruent-to-ABCD-and-prove-that-the-centroids-of-the-same-tr

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Question Number 16072 by Tinkutara last updated on 17/Jun/17 $Let A B C D be a convex quadrilateral .$ $Prove that the orthocenters of the$ $triangles A B C, B C D, C D A and D A B$ $are the vertices of a quadrilateral$ $congruent to A B C D and prove that the$ $centroids of the same triangles are the$ $vertices of a cyclic quadrilateral .$ Commented…

Let-ABCD-be-a-convex-quadrilateral-and-let-E-and-F-be-the-points-of-intersections-of-the-lines-AB-CD-and-AD-BC-respectively-Prove-that-the-midpoints-of-the-segments-AC-BD-and-EF-are-collinear-

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Question Number 16068 by Tinkutara last updated on 21/Jun/17 $Let A B C D be a convex quadrilateral$ $and let E and F be the points of$ $intersections of the lines A B, C D and$ $A D, B C, respectively . Prove that the$ $midpoints of the segments A C, B D,$ $and E F are collinear .$ Answered by ajfour…

In-the-interior-of-a-quadrilateral-ABCD-consider-a-variable-point-P-Prove-that-if-the-sum-of-distances-from-P-to-the-sides-is-constant-then-ABCD-is-a-parallelogram-

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Question Number 16069 by Tinkutara last updated on 21/Jun/17 $In the interior of a quadrilateral$ $A B C D, consider a variable point P .$ $Prove that if the sum of distances from$ $P to the sides is constant, then A B C D$ $is a parallelogram .$ Terms of Service Privacy Policy…

Let-ABCD-be-a-convex-quadrilateral-Prove-that-AB-CD-AD-BC-AC-BD-if-and-only-if-ABCD-is-cyclic-Ptolemy-s-theorem-

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Question Number 16070 by Tinkutara last updated on 21/Jun/17 $Let A B C D be a convex quadrilateral .$ $Prove that$ $A B . C D + A D . B C = A C . B D$ $if and only if A B C D is cyclic ({Ptolemy}^{'} s$ $theorem) .$ Terms of Service Privacy Policy…

Category: Geometry