Question:
In \( \triangle ABC \), \( AD \) is the bisector of \( \angle ABC \), \( AB = 4 \, \text{cm} \), \( AC = 6 \, \text{cm} \), and \( BD = 2 \, \text{cm} \). Find the value of \( DC \).
In \( \triangle ABC \), \( AD \) is the bisector of \( \angle ABC \), \( AB = 4 \, \text{cm} \), \( AC = 6 \, \text{cm} \), and \( BD = 2 \, \text{cm} \). Find the value of \( DC \).
Updated On: Oct 27, 2025
- 3 cm
- 6 cm
- 7 cm
- 4 cm
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
By the Angle Bisector Theorem, we know that the ratio of the two segments formed by the angle bisector on the opposite side is equal to the ratio of the other two sides:
\[
\frac{AB}{AC} = \frac{BD}{DC}
\]
Substituting the known values:
\[
\frac{4}{6} = \frac{2}{DC}
\]
Now, cross multiply to find \( DC \):
\[
4 \times DC = 6 \times 2
\]
\[
4 \times DC = 12
\]
\[
DC = \frac{12}{4} = 3
\]
Thus, the length of \( DC \) is \( \mathbf{3 \, \text{cm}} \).
Correct Answer: (A) \( 3 \, \text{cm} \)
Was this answer helpful?
0
0
Top Questions on Triangles
- If the orthocentre of the triangle formed by the lines $ y = x + 1 $, $ y = 4x - 8 $, and $ y = mx + c $ is at $ (3, -1) $, then $ m - c $ is:
In the adjoining figure, \( AP = 1 \, \text{cm}, \ BP = 2 \, \text{cm}, \ AQ = 1.5 \, \text{cm}, \ AC = 4.5 \, \text{cm} \) Prove that \( \triangle APQ \sim \triangle ABC \).
Hence, find the length of \( PQ \), if \( BC = 3.6 \, \text{cm} \).
- ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
- In \(\triangle DEF\) and \(\triangle PQR\) it is given that \(\angle D = \angle Q\) and \(\angle R = \angle E\), then which of the following is correct?
- In any \(\triangle ABC\), \(\angle A = 90^\circ\), BC = 13 cm, AB = 12 cm; then the value of AC is
View More Questions
Questions Asked in Bihar Class X Board exam
- One day the old emperor Shah Jahan became ill. His son Aurangzeb, who always wanted to be the emperor, put his father in a jail. Jahanara Begum, the eldest child of Shah Jahan, did not leave her father and went to jail along with him. She said, “I shall share the suffering of my father. He needs me in his old age, and I shall never leave him.” Shah Jahan spent seven years in jail before dying. During that period, Princess Jahanara stayed there and took care of him. After the death of her father, she returned to her own palace and continued to live there till her death. Before her death, however, she gave away all she had to the needy and the poor. Upon her death, Aurangzeb gave her the posthumous title : Sahibat-uz-Zamani (mistress of age).
- Bihar Board X - 2025
- Reading Comprehension
- Choose the passive voice of : “Have this lock broken.”
- Choose the most suitable translation : वे लोग विद्यालय जा चुके हैं।
- Bihar Board X - 2025
- Comparative Literature and Translations Studies
- Choose the most suitable translation : उसने मुझे सोया हुआ पाया।
- Bihar Board X - 2025
- Comparative Literature and Translations Studies
- Choose the most suitable translation : नियमित रूप से अध्ययन करो।
- Bihar Board X - 2025
- Comparative Literature and Translations Studies
View More Questions