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Question bank: Triangles: Cevians and Notable Points

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Question 1:

Medium

In a triangle ABC, a cevian is a line that connects a vertex to a point on the opposite side. Consider a triangle ABC, where D is a point on line BC. The segment AD is a cevian of the triangle. Now, suppose point D divides line BC into segments BD and DC, such that their measures are 3 cm and 5 cm, respectively, and the measure of segment AD is 6 cm. Using Stewart's formula for cevians in a triangle, what is the sum of the squares of the lengths of sides AB and AC?

Triangles: Cevians and Notable Points

Question 2:

Very Easy

In a triangle ABC, a cevian is a line segment that connects a vertex of the triangle to any point on the support line of the opposite side. Let P be a point of intersection of the internal angle bisectors of triangle ABC. What is the name given to point P in relation to the cevians of triangle ABC? Justify your answer based on the properties of the notable points of the triangle and the internal angle bisectors.

Triangles: Cevians and Notable Points

Multidisciplinary Question

Question 3:

Easy

The meeting point of the medians is the:

Triangles: Cevians and Notable Points

Contextualized Question

Question 4:

Medium

In a dodgeball game in Physical Education class, the students decided to mark the playing field in the shape of a triangle in the school yard. One of the students drew a cevian connecting vertex A to the opposite side measuring 18 meters. This cevian divides the opposite side into two segments with lengths x and 6. Determine the value of x and the ratio between the sides divided by the cevian.

Triangles: Cevians and Notable Points

Question 5:

Medium

In a triangle ABC, consider D a point on the line BC such that BD/DC = 2. The line AD is a cevian of triangle ABC. Now, consider point E on line AC and point F on line AB in such a way that DE and DF are parallel to BC. If BE/EA = 3 and CF/FB = 4, what is the ratio AF/FE?

Triangles: Cevians and Notable Points

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