Question:medium

The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

Updated On: Jan 13, 2026
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Correct Answer: 2

Solution and Explanation

The given triangle is a right-angled triangle with sides measuring 6, 8, and 10 units.

For a right triangle, the inradius \( r \) can be calculated using the formula:

\[ r = \frac{a + b - c}{2} \] where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.

Plugging in the values \( a = 6 \), \( b = 8 \), and \( c = 10 \):

\[ r = \frac{6 + 8 - 10}{2} = \frac{4}{2} = 2 \]

The inradius is therefore 2 units.

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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