badge image

Enroll For Free Now & Improve Your Performance.

User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.

Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping
Grade: 10


I is the incenter of triangle ABC. X and Y are the feet of the perpendiculars from A to BI and CI. Proove that XY is parallel to BC.

8 months ago

Answers : (2)

25311 Points
Dear student
There is no figure attached.
Please check and repost the question with an image.
I will be happy to help you.
8 months ago
Aditya Gupta
2069 Points
note that aruns ans is illogical, your ques is perfectly fine and doesnt need any pic. correct soln is mentioned below:
first draw the figure.
let BI when extended intersect AC at P and CI when extended intersect AB at Q. obviously X and Y lie on these lines respectively.
by properties of incentre, angle ABI= angle CBI= B/2
angle BCI= angle ACI= C/2
angle BAI= angle CAI= A/2.
now, in tri ABQ,
B/2 + A + angle AQB= 180
or angle AQB= 180 – (A+B/2)
now In tri AXQ,
90 + angle AQB + angle QAX= 180
substitute value of angle AQB, we have
angle QAX= A + B/2 – 90
Hence angle IAX= angle CAI – angle QAX
= A/2 – (A + B/2 – 90)
= 90 – (A+B)/2
= C/2
now, note that quad AYIX is a cyclic quad, since sum of opposite angles is 180 (angle AYI + angle AXI= 90+90= 180). hence a circle can be circumscribed around it. so, angle IYX= angle IAX (by angles in the same segment circle theorem).
so that angle IYX= angle IAX= C/2
but, angle BCI= C/2 too.
so, angle IYX= angle BCI
since angle IYX and angle BCI are alternate interior angles with the common transversal CY, we conclude that their equality implies that BC and XY are parallel.
8 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Course Features

  • 53 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details