Geometry – Page 146

A-triangle-ABC-has-the-following-properties-BC-1-AB-BC-and-that-the-angle-bisector-from-vertex-B-is-also-a-median-Find-all-possible-triangle-s-with-its-their-side-lengths-and-angles-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 112209 by Aina Samuel Temidayo last updated on 06/Sep/20 $A triangle ABC has the following$ $properties BC = 1, AB = BC and that$ $the angle bisector from vertex B is$ $also a median . Find all possible$ $triangle (s) with its / their$ $side - lengths and angles .$ Commented…

Let-denote-the-circumcircle-of-ABC-The-tangent-to-at-A-meets-BC-at-X-Let-the-angle-bisectors-of-AXB-meet-AC-and-AB-at-E-and-F-respectively-D-is-the-foot-of-the-angle-bisector-from-BAC-on-BC-

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Question Number 112199 by Aina Samuel Temidayo last updated on 06/Sep/20 $Let Ω denote the circumcircle of ABC .$ $The tangent to Ω at A meets BC at X .$ $Let the angle bisectors of ∠ AXB meet$ $AC and AB at E and F$ $respectively . D is the foot of the angle$ $bisector from ∠ BAC on BC . Let AD$ $$\mathrm{intersect}\:\mathrm{EF}\:\mathrm{at}\:\mathrm{K}\:\mathrm{and}\:\Omega\:\mathrm{again}\:\mathrm{at} \…

Question-46546

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Question Number 46546 by ajfour last updated on 28/Oct/18 Commented by ajfour last updated on 28/Oct/18 $A c i r c u l a r r i n g o f r a d i u s R, r e s t s$ $a g a i n s t t w o a d j a c e n t w a l l s a n d$ $g r o u n d . I f G (r \cos α, r \sin α, 0),$ $f i n d c o o r d i n a t e s o f P a n d Q$ $$\left({points}\:{of}\:{contact}\:{of}\:{ring}\:{with}\right.…

Question-112076

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Question Number 112076 by I want to learn more last updated on 06/Sep/20 Commented by Aina Samuel Temidayo last updated on 06/Sep/20 $Is OD the angle bisector of D ?$ …

In-a-trapezium-ABCD-with-AB-parallel-to-CD-If-M-is-the-midpoint-of-line-segment-AD-and-P-is-a-point-on-line-BC-such-that-MP-is-perpendicular-to-BC-Show-that-we-need-only-the-lengths-of-line-segme

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Question Number 112060 by Aina Samuel Temidayo last updated on 06/Sep/20 $In a trapezium, ABCD, with AB$ $parallel to CD . If M is the midpoint of$ $line segment AD and P is a point on$ $line BC such that MP is perpendicular$ $to BC . Show that, we need only the$ $lengths of line segments MP and BC$ $$\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{ABCD}. \…

Question-177596

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Question Number 177596 by cherokeesay last updated on 07/Oct/22 Answered by mr W last updated on 07/Oct/22 Commented by mr W last updated on 07/Oct/22…

Using-the-cosine-rule-c-2-a-2-b-2-2abcosC-prove-the-triangle-inequality-if-a-b-and-c-are-sides-of-a-triangle-ABC-then-a-b-c-and-explain-when-equality-holds-Further-prove-that-sin-sin-s

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Question Number 112059 by Aina Samuel Temidayo last updated on 05/Sep/20 $Using the cosine$ $rule (c^{2} = a^{2} + b^{2} - 2 abcosC), prove the$ $triangle inequality : if a, b and c are$ $sides of a triangle ABC, then a + b ⩾ c$ $and explain when equality holds .$ $$\mathrm{Further}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{sin}\:\alpha\:+\:\mathrm{sin}\:\beta\:\geqslant…

Four-spheres-with-radii-a-b-c-and-d-touch-each-other-Find-the-radii-of-their-circumscribed-sphere-R-and-their-inscribed-sphere-r-in-terms-of-a-b-c-and-d-

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Question Number 46481 by MrW3 last updated on 27/Oct/18 $F o u r s p h e r e s w i t h r a d i i a, b, c a n d d$ $t o u c h e a c h o t h e r . F i n d t h e r a d i i o f$ $t h e i r c i r c u m s c r i b e d s p h e r e (R) a n d$ $t h e i r i n s c r i b e d s p h e r e (r) i n t e r m s o f$ $a, b, c a n d d .$ Commented by MJS last updated…

Question-46453

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 46453 by MrW3 last updated on 26/Oct/18 Commented by MrW3 last updated on 27/Oct/18 $T h r e e c i r c l e s w i t h r a d i i a, b a n d c$ $t o u c h e a c h o t h e r . T h e i r c i r c u m s c r i b e d$ $c i r c l e h a s t h e r a d i u s R a n d t h e i r$ $i n s c r i b e d c i r c l e h a s t h e r a d i u s r .$ $${Prove}\:{that}…

Question-111926

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 111926 by ajfour last updated on 05/Sep/20 Commented by ajfour last updated on 05/Sep/20 $I f △ A B C i s e q u i l a t e r a l w i t h s i d e s,$ $f i n d r a d i i o f t h e t h r e e c i r c l e s i n$ $t e r m s o f s .$ Answered by…

Category: Geometry