Question

yjw

求解🙏🙏(第五冊的

3. 如圖,O為五邊形ABCDE之內心,圓Q為其內切圓,且
信AOB為正三角形。
(1) 若AB 三8,EO=/57,求AE的長?
(2) 若/BOC 三70”,求ZBCD的度數?

Answer 1

Ny-Ålesund

※如有錯誤請留言※

(1)
因為 P 點是切點 -> OP 垂直 AB
OP^2 = OA^2 - AP^2 = OB^2 - BP^2
又 OA = OB = AB = 8 --> AP = BP = 8/2 = 4
切線，AP = AQ, BP = BR
--> AQ = 4, BR = 4

OQ^2 = OA^2 - AQ^2 = 64 - 16 = 48

OQ^2 + EQ^2 = OE^2
48 + EQ^2 = 57, EQ = 3
AE = AQ + EQ = 4 + 3 = 7 #

(2)
△BOP 全等 △BOR --> ∠OBR = ∠OBP = 60度
又 ∠BOC = 70度 --> ∠OCB = 180 - 60 - 70 = 50度
∠OCB = ∠OCD = 50度 (因為 △COR 全等 △COS)
∠BCD = 50 + 50 = 100度