High School

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------------------------------------------------ Let triangle ABC have vertices on a circle. Let AD be the altitude and AP be the diameter of the circle. Determine the relationship between AD and AP:

a) AD > AP
b) AD = AP
c) AD < AP

Answer :

Final answer:

The relationship between the altitude of a triangle and the diameter of the circle it is inscribed in depends on the lengths of AD and AP.

Explanation:

The question asks about the relationship between the altitude of a triangle and the diameter of the circle it is inscribed in. Let's analyze the different possibilities:

a) If the altitude AD is greater than the diameter of the circle AP, then we have AD > AP.

b) If the altitude AD is equal to the diameter of the circle AP, then we have AD = AP.

c) If the altitude AD is less than the diameter of the circle AP, then we have AD < AP.

Therefore, the answer is dependent on the actual lengths of AD and AP in relation to each other.

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