1. (Guiyang City, Guizhou Province) As shown in the figure, it is known that AB is a chord of ⊙O, and the radius OA = 2cm∠AOB = 120. (1) Find the value of tan∠OAB; (2) calculate s △ AOB; (3) The last moving point P on ⊙ O moves counterclockwise from point A.. When s △ POA = s △ AOB, find the arc length of point P (regardless of the coincidence of point P and point B). Solution: (1) ∵ OA = OB, ∠ AOB = 6560. ∴∠ OAB = 30∴∠∠∠ OAB = 3 3 .................. If O is OH⊥AB in H, then OH = 2 1 OA = 1, AB = 2 ah = 32 OH = Oh = 2 1× 32× 1 = 3 (cm2) ..........................................................................................................................................∴S△P / Kloc-0/OA=S△AOB, ∠ AOP1= 60 ∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴ ∠ AOP2 = 120 ∴ AP2 ∴ ........................ OP3 with a length of 34π (cm) can easily obtain s △ p3oa = s △ AOB, and ∴ ABP3 ∴ is 3 10 π (cm) ....................................... diagram/. (Nantong City, Jiangsu Province, 20 10) As shown in the figure, in the right-angle ABCD, AB = M (m is a constant greater than 0), BC = 8, and E is the moving point on the BC line (not coincident with B and C). The connecting DE is EF⊥DE, and EF intersects with Reba. (2) If m = 8, what is the value of x and the maximum value of y? (3) If y = m 12, what is the value of m to make △DEF an isosceles triangle? Solution: (1) ∫ ef de, ∴∠ def = 90, ∴∠bef+∠ced = 90∠bef+∞. 8 = mx ∴ y =-m 1x2+M8x ................................ then y =-81x2+x =-81(x-4) 2+2 ∴ when x = 4, the value of y is the largest. The maximum value of y = 2 ... then-m1x 2+M8x = m12 ∴ x2-8x+12 = 0, and the solution is x 1 = 2, x2 = 6...∴. At this time, Rt△BFE≌Rt△CED ∴ When EC = 2, M = CD = BE = 6...M = CD = Be = 2, that is, when the value of M should be 6 or 2, △DEF is ...................................................................................................................................... (2) of isosceles triangle. If point A (x, y) is the moving point on the first quadrant straight line Y = KX- 1, when point A moves, try to write the functional relationship between the area s of △AOB and x; (3) Inquiry: ① When point A moves to what position, the area of △AOB is 41; A B C D E F A B C D E F C O B x y A(x, y) y = kx- 13② If ① holds, is there a little P on the X axis, so that △POA is an isosceles triangle? If yes, please write down the coordinates of all P points that meet the conditions; If it does not exist, please explain why.
Solution:
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