Question:
In \(\triangle ABC\), points \(X\) on \(AB\) and \(Y\) on \(AC\) satisfy \(XY\parallel BC\). If \(AX:XB=2:3\), then \(AY:YC=\) ?
In \(\triangle ABC\), points \(X\) on \(AB\) and \(Y\) on \(AC\) satisfy \(XY\parallel BC\). If \(AX:XB=2:3\), then \(AY:YC=\) ?
Show Hint
When a segment is parallel to a triangle’s side, it divides the other two sides proportionally.
Updated On: Oct 27, 2025
- \(3:2\)
- \(2:3\)
- \(1:3\)
- \(3:1\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
By Basic Proportionality Theorem, \(\dfrac{AX}{XB}=\dfrac{AY}{YC}\). Hence \(AY:YC=2:3\).
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, \( \triangle CAB \) is a right triangle, right angled at A and \( AD \perp BC \). Prove that \( \triangle ADB \sim \triangle CDA \). Further, if \( BC = 10 \text{ cm} \) and \( CD = 2 \text{ cm} \), find the length of } \( AD \).
If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side. State and prove the converse of the above statement.
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 \( BC = 3.6 \, \text{cm} \).
- The perimeters of two similar triangles are 22 cm and 33 cm respectively. If one side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle.
View More Questions
Questions Asked in Bihar Class X Board exam
- Radha's friend says that Radha is deeply hurt and has ........................ weight.
- Bihar Board X - 2025
- Thinner Than a Crescent
- I am proud ........................ my son.
- Bihar Board X - 2025
- Prepositions
- My friend was annoyed ........................ me.
- Bihar Board X - 2025
- Prepositions
- 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 most suitable translation : उसने मुझे सोया हुआ पाया।
- Bihar Board X - 2025
- Comparative Literature and Translations Studies
View More Questions