answer:We have -2-6=-（2+6）=-8. Therefore, the correct answer is boxed{A}.

answer:Given that the intersection point of l_1 and l_2 lies on the circle, by geometric properties, we have l_1 perp l_2. Therefore, 1 cdot k + 3 cdot (-1) = 0, solving this gives k = 3. Thus, the correct answer is boxed{text{(B) } 3}.

answer:1. **Initial Definitions**: - Let ( K ) be an arbitrary curve of constant width ( h ). - Let ( K^{prime} ) be the curve obtained by rotating ( K ) by ( 180^circ ) around the origin ( O ). 2. **Sum of Curves**: - Define ( K^* = K + K^{prime} ) as the sum of ( K ) and ( K^{prime} ). 3. **Constant Width Curve**: - From previous references (specifically, Problem 47, Section 4), the sum ( K^* ) is a curve of constant width ( 2h ). 4. **Central Symmetry**: - The curve ( K^* = K + K^{prime} ) is centrally symmetric about the origin ( O ). This follows because: - Rotating ( K ) by ( 180^circ ) results in ( K^{prime} ). - Thus, ( K^{prime} ) is symmetric to ( K ) about the origin. 5. **Self-Symmetry Under Rotation**: - Given the central symmetry, ( K^* ) remains unchanged under a rotation of ( 180^circ ) around ( O ). 6. **Conclusion: Circular Shape**: - According to Problem 84, any centrally symmetric curve of constant width ( 2h ) that remains unchanged by a ( 180^circ ) rotation must be a circle of radius ( h ). 7. **Length Calculations**: - The length of the circle ( K^* ) with radius ( h ) is ( 2pi h ). - By other geometrical principles (Section 4, page 59), the length of ( K^* ) is also the sum of the lengths of ( K ) and ( K^{prime} ). 8. **Equal Lengths of ( K ) and ( K^{prime} )**: - Since ( K ) is rotated to get ( K^{prime} ), both curves have equal lengths. 9. **Final Length Relations**: - Therefore, if the length of ( K^* ) is ( 2pi h ), and each of ( K ) and ( K^{prime} ) contributes equally to this total length: [ text{Length of } K = text{Length of } K^{prime} = pi h ] 10. **Verifying Theorem Barbier**: - This deduction directly relates to Barbier's theorem, which states that the length of any curve of constant width ( h ) is ( pi h ). # Conclusion: [ boxed{pi h} ]

answer:To analyze each option according to the question's requirement, which is to identify a certain event: - **Option A**: The outcome of Xiao Nan successfully ringing a prize in a ring toss game is dependent on various factors such as skill, chance, and the setup of the game. Therefore, this outcome cannot be guaranteed on every attempt. This makes it a random event, not a certain one. - **Option B**: The success of a member of the Nankai basketball team making a shot from the free-throw line is influenced by the player's skill, physical condition, and possibly external conditions like pressure. As such, it is also a random event because the outcome cannot be predicted with certainty every time. - **Option C**: If there are only two identical red balls in a box, and no other balls, drawing a ball from this box guarantees that the ball drawn will be red. This is because there are no other possibilities available in the outcome space. Thus, drawing a red ball in this scenario is a certain event, as it will happen every time without fail. - **Option D**: A fair dice typically has six faces, numbered from 1 to 6. Rolling such a dice and getting a score of 10 is not possible, as the highest score achievable is 6. This makes it an impossible event, which is the opposite of a certain event. Given these analyses, the only option that describes a certain event, where the outcome is guaranteed to happen, is: boxed{C}