Fun Geometry Problem with Solution #97



٨ x = 30°
٨ 1



(1) ˹ش P ☐ABPD 繠☐ѵ AB = AD = BP = DP BC = BP = DP
͡ҡ ѧҠ∠DBP = 45° ∠CBP = 60°

(2)∵BC = BP Р∠CBP = 60° ∆BCP 繠∆ҹ BP = CP Р∠BPC = 60°
ѧࡵ BP = CP = DP ش P 繨شٹҧͧǧՠ∆BCD Ṻ ∠BDC = (∠BPC)/2 x = 30° Q.E.D.

٨ 2



AB (= AD = BC) = a

(1) ˹ش P Шش Q ☐ADQP 繠☐ҡ ըش C 躹 PQ ...
AP = DQ
PQ = AD PQ = a
∠ADQ =∠APQ =∠DQP = 90°

(2)∵AB = AD ∆ABD 繠∆˹Ҩ ՠ∠A (= 90°) ʹ ∠ABD = 45°(∠CBP = 30°) Р∠ADB = 45°(∠BDQ = 45°)
∵ AB = BC ∆ABC 繠∆˹Ҩ ՠ∠B (= 150°) ʹ ∠BAC (=∠ACB) = 15°

(3) Ҡ∆BCP 繠∆ҡ ՠ∠P ҡ Р∠B = 30° CP = BC/2 CP = a/2 CQ = a/2
ѧࡵҠ∆CDQ∆ACP ¤ѹẺ -- (DQ = AP,∠CQD =∠APC, CQ = CP) ∠CDQ =∠CAP ∠CDQ = 15° ∠BDC = x = 30° Q.E.D.




Create Date : 06 Ҿѹ 2558
Last Update : 6 Ҿѹ 2558 0:00:00 .
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