HMMT 十一月 2009 · 冲刺赛 · 第 12 题
HMMT November 2009 — Guts Round — Problem 12
题目详情
- [ 8 ] Let ω be a circle of radius 1 centered at O . Let B be a point on ω , and let l be the line tangent to
°
ω at B . Let A be on l such that ∠ AOB = 60 . Let C be the foot of the perpendicular from B to OA .
Find the length of line segment OC .
2 ANNUAL HARVARD-MIT NOVEMBER TOURNAMENT, 7 NOVEMBER 2009 — GUTS ROUNDnd
英文原题
[ 8 ] Let ω be a circle of radius 1 centered at O . Let B be a point on ω , and let l be the line tangent to
ω at B . Let A be on l such that ∠ AOB = 60 ◦ . Let C be the foot of the perpendicular from B to OA .
Find the length of line segment OC .
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2 nd ANNUAL HARVARD-MIT NOVEMBER TOURNAMENT, 7 NOVEMBER 2009 — GUTS ROUND
解析
英文解析
- [ 8 ] Let ω be a circle of radius 1 centered at O . Let B be a point on ω , and let l be the line tangent to
°
ω at B . Let A be on l such that ∠ AOB = 60 . Let C be the foot of the perpendicular from B to OA .
Find the length of line segment OC .
1 ° 1
Answer: We have OC/OB = cos(60 ). Since OB = 1, OC = .
2 2
2 ANNUAL HARVARD-MIT NOVEMBER TOURNAMENT, 7 NOVEMBER 2009 — GUTS ROUNDnd