【压轴题打卡434：圆有关的几何综合问题】
已知：A、B、C不在同一直线上.
（1）若点A、B、C均在半径为R的⊙O上，
i）如图一，当∠A=45°时，R=1，求∠BOC的度数和BC的长度；
ii）如图二，当∠A为锐角时，求证sin∠A=BC/2R；
（2）.若定长线段BC的两个端点分别在∠MAN的两边AM、AN（B、C均与点A不重合）滑动，如图三，当∠MAN=60°，BC=2时，分别作BP⊥AM，CP⊥AN，交点为点P ，试探索：在整个滑动过程中，P、A两点的距离是否保持不变？请说明理由.

#学科大挑战# #在微博过暑假#

射击距离对弹道散布的影响[酷]
☞由于特种兵们在射击时需要压枪，弹道的垂直散布和水平散布近似（h≈s）在此只研究垂直散布。
距离对散布的影响（在弹道未下降之前，子弹水平射出）。将PQ看作近处射击靶位，BC看作远处射击靶位↓
如图,在等腰△ABC中,P、Q分别为腰AB和腰AC上的两点,且PQ∥BC,AN⊥BC于N,交PQ于M.经测量,AM＝1180,MN=650.（测量单位：像素）
易得：△ABC∽△APQ
∴BC：PQ=AN：AM
∵AM=1180，MN=650
∴AN＝1830
∴AN：AM＝1830：1180≈1.551
∴BC：PQ≈1.551
即远处射击靶位的垂直弹道散布大约增加到了近处靶位的1.551倍。
☞根据相似三角形的相似比，当射击距离扩大倍时，垂直散布距离（h）也会扩大倍。考虑到水平散布（s），整个弹道散布面的面积会扩大²倍。 https://t.cn/z86CIg1

Happy Birthday :) 1 year old. making and releasing this album was probably one of the most difficult things i’ve done. on an emotional level bc it’s all personal and stuff. but also bc of this pandemic. releasing something you put your whole heart into in such uncertain times is…incredibly scary. thank you all for embracing it and turning what was such a daunting prospect into the wildest ride of our lives…even though we haven’t actually been able to ride anywhere at all and i’ve just been sitting in my studio in my undies eating cereal for 18 months. will be putting lots more highlights and memories out over the next week (the main thing for me was seeing/hearing artwork/remixes/writing that came back from you all…warmed our hearts so much when we couldn’t come see you all on tour.) but today…we are releasing a very limited amount of pop-out gatefold dreamland records pressed to semi-transparent vinyl. link https://t.cn/A6Iy1nVb , first come first served. thank u blood records for helping us create this. xx