The review is comprehensive and well presented. Giving formulae together with proof is much appreciated as knowning 'why' is as important as knowing 'how'. I would like to share a few points for the sake of students. 1. Formulae for inradius r and circumradius R are used together with Heron's formulae which gives area of triangle in formulae using given sides a, b, c: inradius r = area of triangle/semi-perimenter (S = 1/2 (a + b + c), circumradius R = abc/4 x area of triangle (Formula can be proved by area equation: area = (1/2) absinC and 2R = c/sinC) 2. Proof of angle bisector theorem can be done without using sine rule which needs further proof. With usual notation of triangle A, B, C for angles and a, b, c for sides. Let D be the point of intersection on side a formed with angle bisector from angle A, dividing side a into a1 near C and a2 near B. Prove b/a2 = c/a1 as the angle bisector theorem as follows: Areas of triangles ABD and ACD have ratio a2/a1 by equal height triangles with bases a2 & a1. Angle A is divided into two A/2 angles by the angle bisector. Areas of triangles ABD and ACD can be found alternatively using height bsinA/2 from angle B and height csinA/2 from angle C, with line AD as the base for both triangles. Hence the area ratio is b:c which is equal to a2:a1. The usual form of angle bisector theorem b/a2 = c/a1 is established.
恻隐之心，羞惡之心，辭讓之心，是非之心
中文四心😂
中文一心
问：孟子之四心有那些？
答：形 垂 外 内
死去的中文正在攻擊我
中國傳統文化
唔係講笑..完全係教師級既四心教學 仲教得清晰過我補習吖sir~感謝你呢個素未謀面既老師❤❤
The review is comprehensive and well presented. Giving formulae together with proof is much appreciated as knowning 'why' is as important as knowing 'how'. I would like to share a few points for the sake of students.
1. Formulae for inradius r and circumradius R are used together with Heron's formulae which gives area of triangle in formulae using given sides a, b, c: inradius r = area of triangle/semi-perimenter (S = 1/2 (a + b + c), circumradius R = abc/4 x area of triangle (Formula can be proved by area equation: area = (1/2) absinC and 2R = c/sinC)
2. Proof of angle bisector theorem can be done without using sine rule which needs further
proof. With usual notation of triangle A, B, C for angles and a, b, c for sides. Let D be the point of intersection on side a formed with angle bisector from angle A, dividing side a into a1 near C and a2 near B. Prove b/a2 = c/a1 as the angle bisector theorem as follows: Areas of triangles ABD and ACD have ratio a2/a1 by equal height triangles with bases a2 & a1.
Angle A is divided into two A/2 angles by the angle bisector. Areas of triangles ABD and ACD can be found alternatively using height bsinA/2 from angle B and height csinA/2 from angle C, with line AD as the base for both triangles. Hence the area ratio is b:c which is equal to a2:a1. The usual form of angle bisector theorem b/a2 = c/a1 is established.
多謝你教識我四心點做 mc真係出左 雖然我最後錯左
咁啱呀
只能說 師兄好有心🎉
Joseph 撞到 k sir????????????????????????
等你拍片貼題🐰
akira到此一遊
已經諗好今晚睇舊版四心絕技 多謝師兄🙏
四心呢樣野最詭異既一點係 佢竟然係一個中三課題，而且成個高中三年時間係完全唔會再教（除非你學校老師/補習老師肯專登教返）
中三教四心果陣大多數學校都只會教最基本既定義同特性（邊條線同邊個心有關），但去到中六考DSE竟然係會考一大堆隱藏特性（比如pr=2a , centroid座標=三點座標加埋除3） 所以好多學生會覺得自己好似完全冇學過四心呢課咁。
根本呢課唔應該中三教，搬去中五中六教就合理好多
早識早享受
中三老師：高中會再教，而家唔講咁多
高中老師：中三你哋咪學咗囉，我唔教多次
素未謀面的恩師🙏
多謝晒你！啲concept依家好清🥹🩵
如果比orthocenter 同三角形另外兩點，可以入呢三點入program，program show 嗰個orthocenter 係淨返嗰點
多謝你🍀🌟🌟💜🙇🏻♀️🙏🏻希望有5/以上 如果有就入到我最鍾意嗰科🥹 共勉
真係多謝曬
特別係第41題問四心四線共線
好彩睇曬條片然後直接秒殺
最終個分攞到42/45🎉
好癲，考試前夕睇，希望part B有救❤
實在教得太好了
真係多謝你🙏
clssss🥹🩷救星 超有心～thankyouuu
32:58 let o be the orthocentre 如果搵 CG 同 CO 嘅 slope 再 check 係咪一樣 係咪一樣得？
yesss! 如果到時有coordinates，然後要prove collinear的話，用slope prove嘅機會好大！
2024朋友們❤️
Good effort🫡
33:31 口誤😂係因為corresponding angle congruent triangle, 黑線藍線parallel先係alternate angle equal😌
ohhhh!!! 係corresponding angles of similar triangles! 感謝🙏
好眼訓，決定聽日食早餐個陣睇
好好，都幾齊
今年的dser有福了
感謝❤
感謝🙏❤
謝謝 frankie sir 😭
好正❤❤❤❤🎉🎉🎉
好有用🙌🏻🙌🏻🙌🏻會唔會講埋3D🙏🏻
其實in centre a:c=b:d M2 2022出左🎉
YES!! 心水清！
2022一句using the fact that真係唔係幾開心！期待佢出proof！
多謝🙏
可唔可以出埋3D thxx
正❤
痴線 點解以前冇人同我講啲咁嘅嘢 anyway thanks a lot!!
🎉
請問如果想33:30嗰兩個triangles 要唔要用ratio of 2 sides including angle prove or 淨係寫佢地係similar without the proving process?
視乎題目！
如果題目字眼係"Prove that"或者"Show that" 咁就要寫清楚ratio of 2 sides, inc. angles
但如果題目只係"Find" 或者 "Do you agree" 的話，直接寫similar就可以了
@@frankiemak9590 thank you
有冇呢份筆記?🙏
重製版都出埋 有feel🙏
請問可唔可以要份notes👉🏼👈🏼
感謝🙏師兄
Circumcenter既公式a/sinA=2r
配合Area=1/2(bcsinA)
會變成Area=abc/4r
Frankie sir得閒既話可以加埋落去
唔知今年part b會唔會玩呢個prove
有趣喎！我都無諗過呢樣！多謝分享😆
22:10 M2有出過
yes!! 期待佢core出proof同埋用嚟搵in-centre!
impressive
🙏
請問centroid條式考dse用係咪都會比分？因為教課書無教。
教科書有教1:2呢個特性，所以用返mid point同section formula嘅concepts去寫條式就最穩陣，例如三點嘅x-coordinates分別係a,b,c，咁centroid嘅x-coordinate就係 ( (a+b)/2*2 + c ) / 3，即係條片裡面所提到證明條公式嘅方法，咁就解釋得清清楚楚，又無用到out-syl嘅公式啦！
請問， 可不可以一開卷。就直接先做最後一題？
我自己就唔建議，個腦都需要熱身！不過如果呢個係你嘅習慣，咁就照做！
想問ASGS文字題唔會無啦啦出返section B？aim high嘅話使唔使溫埋？🙏🏻🙏🏻🙏🏻
Aim lv5或以上就要溫埋2012同2013嘅ASGS + 2014嘅probability！加油！
如要用a/sinA =2r 洗唔洗prove 左先？
如果題目真係出 prove that a/sin A = 2r，咁就要寫齊reason咁prove
但如果做緊四心/equation of circle/3D，想用條式搵radius的話，就唔需要寫reason，粗略寫多一行中間隻角 = 2A，所以 sin A = a/(2r) 就已經ok！
2024貼中咗
都冇出四心
@@oxcow99有出
第41題
但出得好簡單
主要係片入面講咗共線
嗰題直接秒殺
@@OwO-j4w 果題有伏，其中一點唔係四心而係vertex 🤣 只係背左「四心共線」既同學好易中招
@@oxcow99 我就係咁啱好
記得條片
咁啱冇中伏🤣
有沒有呢份筆記????
請問可否出一段video 講吓佛家同埋墨家思想🙏
佛家可以睇住呢個先！
ua-cam.com/video/DBZRdacHUfk/v-deo.html
日後有機會都可能會出佛家嘅片！但就未必好exam-oriented
墨家我自己淨係識兼愛非攻，講唔到太詳細了😶🌫
i love you
😮😮😮