Large Angle
How large is angle CKA?
Triangle ABC has angles A=72°, B=60°, C=48°.
A circle is inscribed in a triangle ABC. The circle touches AB and BC at points E and F, respectively. Angle bisector A intersects line EF at point K.
The answer is angle(CKA) = 90°.
Let I is the incenter of ∆ABC (intersection point of angle bisectors of A and B). Since both tangents from B to the incircle are equal, ∆BEF is equilateral hence
angle(AEF) = angle(AEK) = 120°, angle(BAK) = 36°, angle(AKE) = 24°
Consider ∆AEK and ∆AIC:
angle(EAK) = angle(IAC) = 36°, angle(AKE) = angle(ACI) = 24°,
angle(AEK) = angle(AIC) = 120°, i.e. they are similar, the coefficient of similarity is
| AE | : | AI | = cos 36° (∆AEI is right)
Then also | AK | : | AC | = cos 36°, but the latter is possible only if ∆AKC is right.
By the way K is outside ∆ABC because the line AK intersects BC in a point let’s say A’ such that ∆ABA’ has angles 36°, 60°, 84° and IF as inradius is perpendicular to BC.
Sanyo Xacti HD700 with CHEAP wide angle adapter II
|
|
Large Door Scope Door Viewer / Peep Sight Wide Angle IN $3.04 |
|
|
(((PELLA)))SLIDING PATIO DOOR-PANEL RETAINER CLIP & RETAINER ANGLE $9.99 |
|
|
Large DoorScope 5 Colors ABS Wide Angle Door Viewer $15.99 |
|
|
Large DoorScope 5 Colors ABS Wide Angle Door Viewer $15.99 |
|
|
Large DoorScope 5 Colors ABS Wide Angle Door Viewer $15.99 |
|
|
38″ ASB WHITE NEO ANGLE CORNER BATHROOM SHOWER ENCLOSURE W/ THREE LARGE SHELVES $699.99 |
|
|
3M, 4 Pack, Large Area Fine Flexible Angled Sanding Sponge $13.42 |
|
|
3M, 4 Pack, Large Area Medium Flexible Angled Sanding Sponge $13.42 |
|
|
3M, 4pk, 2.5″ x 4.5″, Large Angled Fine Grit Sandblaster Drywall Sanding Sponge $12.63 |
|
|
Large DoorScope 3 Colors Metal Wide Angle Door Viewer $22.99 |
|
|
Large DoorScope 3 Colors Metal Wide Angle Door Viewer $22.99 |
|
|
Large DoorScope 3 Colors Metal Wide Angle Door Viewer $22.99 |
|
|
OXO Good Grips Silicone Pastry Brush $5.49 Silicone Pastry Brush, Gaps In Center Bristles Hold Liquids For Easy Pickup & Release, Tapered Outer Bristles Glide Gently Over Pastries, Heat Resistant To 600 Degree Fahrenheit, Bristles Will Not Scorch, Clump Or Frizz, Easy To Clean…. |
|
|
Fiskars 7861 Axe and Knife Sharpener $7.80 The Fiskars axe and knife sharpener features a patented ceramic wheel to effectively and easily sharpen axes and knives at an exact 30-degree angle. The sharpener is built for safety as well, with a built-in hand guard and non-slip feet. It is covered by a lifetime warranty…. |
|
|
Smith Abrasives CCKS 2-Step Knife Sharpener $1.35 Ceramic and carbide grade. Includes ceramic rods non-slip rubber feet plastic holder and carbide cutting heads. This features 2 tungsten carbide cutting heads whose pre-set angles ensure the perfect edge every time. 3-4 strokes restores the edge.ATTRIBUTES Material: Carbide & Ceramic Special Features: Non-Skid Base for Stable Sharpening Crossed Carbide Blades Provide Quick Edge… |
|
|
The original Three Tenors Concert (Carreras Domingo Pavarotti in Concert Mehta) $2.00 These are the three tenors in concert…. |
|
|
Smith’s PP1 Pocket Pal Multifunction Sharpener $7.03 ATTRIBUTES Grit: Coarse/Medium Material: Carbide Ceramic & Diamond Special Features: Tapered Diamond Rod For Sharpening Serrated and Straight Edges Carbide Blades Quickly Set Your Edge Ceramic Stones Give You A Razor Sharp Edge Reversible and Replaceable Carbide Blades and Ceramic Stones Lanyard Hole Type: Hand Held… |
|
|
Belkin BE112230-08 12-Outlet Home/Office Surge Protector with Telephone and Coaxial Protection $16.00 SAFETY COVERS FOR OUTLETSSLIM DESIGN FOR COMPACT STORAGEORGANIZES CABLES WITH DETACHABLE CORD MANAGEMENT CLIPFLAT-PROFILE PLUG12 OUTLETSTELEPHONE & COAXIAL PROTECTION3780 JOULES8-FT POWER CORDLIFETIME WARRANTY$300000 CONNECTED EQUIPMENT WARRANTYUPC : 722868594322Shipping Dimensions : 14.75in X 6.00in X 2.00inEstimated Shipping Weight : 2.15… |
|
|
AccuSharp 001 Knife Sharpener $4.99 This knife shapener sharpens any double edge blade whether serrated or plain, thick or thin and it will do it faster than youd believe possible. AccuSharp sharpeners are the best, easiest and fastest sharpeners around. The difference is in the specially formulated, precision ground and mounted tungsten carbide blades…. |
|
|
The Simpsons: The Fourteenth Season $18.94 All 22 episodes from season 14–including “Treehouse of Horror XIII,” “Large Marge,” “The Dad Who Knew Too Little,” “C.E. D’oh,” and “Moe Baby Blues”–are featured in a four-disc set. 8 hrs. total. Standard; Soundtracks: English Dolby Digital 5.1, French Dolby Digital Surround, Spanish Dolby Digital Surround; Subtitles: English (SDH), Spanish; audio commentary; featurettes; deleted scenes; art gal… |
|
|
Infiniti Pro by Conair Spin Air Rotating Styler … |
|
|
John Frieda JFHA5 Hot Air Brush $32.88 ADVANCED IONIC TECHNOLOGY PROVIDES UP TO 50% MORE IONS2 HEAT SETTINGS PLUS COOL SETTINGTITANIUM CERAMIC-COATED BARRELENHANCED AIR CONTROLSWIVEL CORDUPC : 074108254177Shipping Dimensions : 3.25in X 5.00in X 14.50inEstimated Shipping Weight : 1.4194… |
This entry was posted on Sunday, September 28th, 2008 at 9:59 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.