Geometry – Page 216

Question-150517

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 150517 by ajfour last updated on 13/Aug/21 Commented by ajfour last updated on 13/Aug/21 $C a n n o t O P b e a b i t g r e a t e r$ $t h a n O B = R (r a d i u s o f h e m i -$ $s p h e r e) ? I f y e s t h e n f o r w h a t$ $r a n g e o f s e m i - v e r t i c a l ∠ θ$ $${of}\:{cone}\:\left({right}\right),\:{is}\:{that}\:{so}?…

Question-84970

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 84970 by Power last updated on 18/Mar/20 Answered by mr W last updated on 18/Mar/20 $2 x + 3 y = π$ $\Rightarrow x = \frac{π}{2} - \frac{3 y}{2}$ $\frac{A B}{\sin (x + y)} = \frac{B D}{\sin x}$ $$\Rightarrow\frac{\mathrm{11}}{\mathrm{cos}\:\frac{{y}}{\mathrm{2}}}=\frac{\mathrm{2}}{\mathrm{cos}\:\frac{\mathrm{3}{y}}{\mathrm{2}}} \…

PS-is-a-line-segment-of-length-4-and-O-is-the-midpoint-of-PS-A-semicircular-arc-is-drawn-with-PS-as-diameter-Let-X-be-the-midpoint-of-this-arc-Q-and-R-are-points-on-the-arc-PXS-such-that-QR-is-para

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 19415 by Tinkutara last updated on 10/Aug/17 $P S is a line segment of length 4 and O$ $is the midpoint of P S . A semicircular$ $arc is drawn with P S as diameter . Let$ $X be the midpoint of this arc . Q and R$ $are points on the arc P X S such that Q R$ $is parallel to P S and the semicircular$ $arc drawn with Q R as diameter is$ $$\mathrm{tangent}\:\mathrm{to}\:{PS}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \…

Question-19394

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 19394 by tawa tawa last updated on 10/Aug/17 Answered by allizzwell23 last updated on 10/Aug/17 $\frac{AB}{DF} = \frac{AC}{CE} similar triangles$ $Let AD = x \Rightarrow BF = x ∴ AB = 6 + 2 x$ $$\:\:\frac{\mathrm{2x}+\mathrm{6}}{\mathrm{6}}\:=\:\frac{\mathrm{20}}{\mathrm{12}}\:\:\:\:\Rightarrow\:\mathrm{2x}+\mathrm{6}\:=\:\frac{\mathrm{20}}{\mathrm{12}}×\mathrm{6}\:=\:\mathrm{10} \…

related-to-Q-19333-the-side-lengthes-of-a-triangle-are-integer-if-the-perimeter-of-the-triangle-is-100-how-many-different-triangles-exist-what-is-the-maximum-area-of-them-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 19388 by mrW1 last updated on 10/Aug/17 $related to Q . 19333$ $the side lengthes of a triangle are$ $integer . if the perimeter of the triangle$ $is 100, how many different triangles$ $exist ? what is the maximum area of$ $them ?$ Commented by mrW1…

Question-150451

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 150451 by ajfour last updated on 12/Aug/21 Commented by Ar Brandon last updated on 12/Aug/21 $I admire your posts sir . Sadly I have very little knowledge$ $on geometry . {You}^{'} re so advanced . Hahaha! I hope I will get$ $there someday .$ Commented…

Question-84899

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 84899 by Power last updated on 17/Mar/20 Commented by Tony Lin last updated on 17/Mar/20 $A (A D E) = 9$ $\Rightarrow h = 6$ $A (E F C)$ $$=\frac{\mathrm{1}}{\mathrm{2}}×{EC}×\left({h}×\frac{\mathrm{6}}{\mathrm{7}}\right) \…

Question-84892

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 84892 by Power last updated on 17/Mar/20 Commented by Power last updated on 17/Mar/20 $please see$ Commented by Power last updated on…

Question-150418

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 150418 by ajfour last updated on 12/Aug/21 Commented by ajfour last updated on 12/Aug/21 $F o r t e t r a h e d r o n e d g e a,$ $a n d s p h e r e r a d i u s r, f i n d$ $f r a c t i o n a l v o l u m e o f s p h e r e$ $w i t h i n t h e t e t r a h e d r o n .$ $${f}=\begin{cases}{{g}_{\mathrm{1}}…

Question-150376

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 150376 by cherokeesay last updated on 11/Aug/21 Commented by liberty last updated on 12/Aug/21 ${(2 \sqrt{3} + r)}^{2} = {(4 \sqrt{3} - r)}^{2} + {(2 \sqrt{3} - r)}^{2}$ $let 2 \sqrt{3} = a$ $$\Rightarrow\left({a}+{r}\right)^{\mathrm{2}} −\left({a}−{r}\right)^{\mathrm{2}} =\left(\mathrm{2}{a}−{r}\right)^{\mathrm{2}}…

Category: Geometry