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61.已知 a,b,c 三数满足条件0≤a≤1≤b≤2≤c≤3.问以 a,b,c 为边的三角形的最大面积等于多少?62.设三角形 a 边上的高 h_a≥a,b 边上的高 h_b≥b.求此三角形三个内角的大小?63.△ABC 的三条高线相交于 O 点,已知 OC=AB,求∠C 的大小?64.飞机沿着中心位于 A 点的圆形轨道飞行,轨道半径10公里,飞行速度1000公里/小时.设某时刻从A 点发射出一支火箭,在整个飞行时间内,控制火箭的速度总等于飞机的速度,火箭的位置总在飞机所在位置和轨道中心 A 的联结线上.问火箭发射后经过多少时间才击中飞机?65.在平面上固定一点 P,考虑所有可能的正三角形 ABC,它们满足条件 AP=3,BP=2.问 CP 的最大
61. It is known that the three numbers of a, b, and c satisfy the condition 0 ≤ a ≤ 1 ≤ b ≤ 2 ≤ c ≤ 3. What is the maximum area of a triangle with a, b, c as an edge? 62. Let triangle a be a side On the high h_a≥a, b on the side of the high h_b≥b. Find the size of the three internal angles of this triangle? 63. The three high lines of ABC intersect at the O point, known as OC=AB, find the size of C? 64. The aircraft flies along a circular orbit centered on point A with an orbit radius of 10 km and a speed of 1,000 km/h. A rocket is fired from point A at a certain time, controlling the speed of the rocket throughout the entire flight time. Equal to the speed of the aircraft, the rocket’s position is always on the connecting line between the aircraft’s position and the center A of the track. Ask how much time has elapsed since the launch of the rocket to hit the plane? 65. Fix a point P on the plane, considering all possible positive triangles ABC They satisfy the condition AP=3, BP=2.