Ceva's Theorem

Q.

State and prove converse of BPT (basic proportionality theorem).

Q. In the given figure, Suppose AB, AC and BC have lengths 13 cm, 14 cm and 15 cm respectively. If $\frac{AF}{FB}=\frac{3}{8}and\frac{CE}{EA}=\frac{6}{9}$, then find BD and DC.

1. 9 cm and 6 cm
2. 8 cm and 7 cm
3. 10 cm and 5 cm
4. 12 cm and 3 cm

Q. Question 4

To construct a triangle similar to a given $\Delta$ABC with its sides of $\frac{3}{7}$ the corresponding sides of $\Delta$ ABC , first draw a ray BX such that $\angle$CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate point $B_1,B_2,B_3....$ on BX at equal distances and next step is to join
(A) $B_{10}$ to C
(B) $B_3$ to C
(C) $B_7$ to C​​​​​​​
(D) $B_4$ to C​​​​​​​

Q. In the given figure, Suppose AB, AC and BC have lengths 10 cm, 11 cm and 12 cm respectively. If $\frac{BD}{DC}=\frac{5}{6}and\frac{CE}{EA}=\frac{3}{10}$, then find AF and FB.

1. 2 cm and 8 cm
2. 8 cm and 2 cm
3. 6 cm and 4 cm
4. 5 cm and 5 cm

Q. In the given figure, Suppose AB, AC and BC have lengths 13 cm, 14 cm and 16 cm respectively. If $\frac{AF}{FB}=\frac{4}{5}and\frac{CE}{EA}=\frac{10}{8}$, then find BD and DC.

1. 7 cm and 9 cm
2. 9 cm and 7 cm
3. 10 cm and 6 cm
4. 8 cm and 8 cm

Q. In the figure given below, 𝐷𝐸∥𝐵𝐶. Find the length of side 𝐴𝐷, given that 𝐴𝐸 = 1.8 𝑐𝑚, 𝐵𝐷 = 7.2 𝑐𝑚 and 𝐶𝐸 = 5.4 𝑐𝑚.

Q. A _____ is a line segment which joins a vertex of a triangle with a point on the opposite side.

1. incircle
2. cevian
3. circle
4. vertex

Q.

In the figure, the medians BD & CE of a ∆ ABC meet at G. Find the ratio of GD : GB.

1. 1/4

2. 3/4

3. 1/2
   

4. 2

5. 1

Q.

In the given figure $ DE\left|\right|BC$. Find $ EC$.

1.5 cm D 1cm E C 

Q. In $\Delta PQR$, $XY\parallel QR$ and $\frac{PX}{XQ}=\frac{2}{3}$ $PY=4cm$ then $YR=$ ?

1. $9cm$
2. $5cm$
3. $8cm$
4. $6cm$

Q. Apply Ceva's theorem and find the value of $x$.

1. 120
2. 240
3. 360
4. 480

Q. Apply Ceva's theorem and find the value of $y$.

1. 20
2. 30
3. 50
4. 40

Q. Ceva's theorem states that $\frac{AF}{FB}.\frac{X}{DC}.\frac{CE}{EA}=1$. Find X.

1. $BF$
2. $BA$
3. $BD$
4. $BC$

Q. A triangle is constructed as shown in the figure below.

Which of the following statement is/are incorrect about $\Delta$ DEF?

1. All its sides are equal
2. It is an isosceles triangle
3. It is a scalene triangle
4. It is not an equilateral triangle

Q.

In a ΔABC, if DE∥BC, prove that AB/AD=AC/AE.

Q. Ceva's theorem states that $\frac{AF}{FB}.\frac{BD}{DC}.\frac{X}{EA}=1$. Find X.

1. EC
2. CE
3. EB
4. BC

Q. Ceva's theorem states that $\frac{AF}{X}.\frac{BD}{DC}.\frac{CE}{EA}=1$. Find X.

1. BF
2. AB
3. FB
4. FP