圆中最值的十种求法（Ten methods of finding the best value in a circle）.doc

圆中最值的十种求法（Ten methods of finding the best value in a circle） Own collection Think its useful So upload it to Baidu Share it with everyone! Ten methods of finding the best value in a circle Experimental junior middle school (223700), Jiangsu County, Siyang province (Zhu Yixin) Seeking the best value in the circle is a common question in the entrance examination It is also a hot and difficult problem in the entrance examination Some students feel helpless about seeking the most valuable question The main reason is that little is known about the method of seeking the best The train of thought is not flexible enough Summarized as follows: First, we use symmetry to find the best value Figure 1.: the O radius is 2 A, B, C in the O OA group of OB Angle AOC=60 degrees P is a fixed point on OB Find the minimum value of PA+PC [analysis]: AO / O to D extension Connect CD * O in P That is, the minimum PA+PC at this time And the minimum value of PA+PC is equal to the length of the string CD Solution: to extend the AO * O in D Connect CD to OB in P Connect PA O OE group of CD Pedal for E In a OCD Because of / AOC=60 / D= / C=30 ~ ~ so In the Rt ODE Delta cos30 = DEG That is, DE=2 x cos30 degrees = so CD=2DE=2 That is, the minimum value of PA+PC is 2. Two, use the shortest section of the vertical line for the most value 2. as shown in the Cartesian coordinate system Coordinate for A (3, 2) The radius is 1 A P is a fixed point on the X axis PQ / A Q to cut The minimum length of the PQ is [analysis]: connect AQ, PA The AQ group of PQ. in Rt Delta PQA PQ= The minimum value of the PQ is converted to the minimum value of the PA According to the vertical line, the minimum minimum value of PA is 2. Solution: connect PA, QA Because the A Q PQ cut in PQ AQ so far In the Rt APQ Delta PQ2=PA2AQ2 PQ= Because A (3, 2) According to the shortest line So the minimum value of PA is 2 So the minimum value of PQ =? Three, use the shortest line between two points to find the most value