In triangle ABC, the medians AD and BE intersect at G. A line DF is drawn parallel to BE such that F is on AC. If AC = 9 cm, then what is CF equal to?
2.25 cm
Concept:
Median: A line segment that joins a vertex to the mid-point of the
the side that is opposite to that vertex
Basic proportionality theorem(BPT): If a line is drawn parallel to
one side of a triangle intersecting the other two sides in distinct
points, then the other two sides are divided in the same ratio.
Calculation:

Given that,
AD and BE are medians of BC and AC respectively.
⇒ BC = 2DC ------(1)
Also, we have AC = 9 cm
⇒ AE = EC = 9/2 = 4.5
In triangle CBE, DF ∥ BE
Using the Basic proportionality theorem
⇒ \(\frac{DC}{BC} = \frac{FC}{EC}\)
⇒ \(\frac{DC}{2DC} = \frac{FC}{4.5}\)
⇒ FC = 4.5/2 = 2.25 cm
∴ CF = 2.25 cm.
What is the area of quadrilateral ABCD?
ABC is a triangle right angled at B. Let D be the midpoint on AC. If BD = 6.5 cm, then what is AB 2 + BC 2 equal to?
Consider the following statements :
1. The sum of any two sides of a triangle is less than twice the median drawn to the third side.
2. The perimeter of a triangle is greater than the sum of the three medians.
Which of the above statements is/are correct?
Two isosceles triangles have equal vertical angles and their areas are in the ratio 4.84 ∶ 5.29. What is the ratio of their corresponding heights?
Δ ABC is similar to Δ DEF. The perimeters of Δ ABC and Δ DEF are 40 cm and 30 cm respectively. What is the ratio of (BC + CA) to (EF + FD) equal to?
ABC is a triangle right angled at C. Let p be the length of the perpendicular drawn from C on AB. If BC = 6 cm and CA = 8 cm, then what is the value of p?
What is the maximum number of circum-circles that a triangle can have?
ABC is a triangle right angled at C with BC = a and AC = b. If p is the length of the perpendicular from C on AB, then which one of the following is correct?
Which of the following is correct?
Which one of the following is correct?
G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
What is the area of quadrilateral ABCD?
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio: