Circle Problem

JOHNLAM17

                               
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I want to ask question Ai
Thz for helping.
其實我已經完成這題，只是想知道有沒有更方便快捷的方法。

[ 本帖最後由 JOHNLAM17 於 19/6/2006 20:47 編輯 ]

抹茶可樂

呢條咪係(..........)我在戰場做果條

應該沒更快的方法了

sapphire

我的方法,不知和你的是否一樣 (或許比你的更慢卅▽卅)

Since H is orthocentre of △ABC, ∠AOC=90°
∠BCS=90° (∠ in semi-circle)
∠AOC+∠BCS=180°
∴AH//SC

Produce CH and meet at AB. Let Z be their intersection.
Since H is orthocentre of △ABC, ∠AZC=90°
∠AZC=∠SCB
∠ZAC=∠CSB (∠s in same seg.)
∴△AZC～△SCA (AA)

∠ACZ=∠SBC (corr. ∠s, ～△s)
∠SAC=∠SBC (∠s in same seg.)
∠SAC=∠ACZ
∴AS//HC
Since AS//HC and AH//SC, AHCS is a //gram.