kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
9.17 Incentre of a Triangle

To find the coordinates of the incentre of a triangle whose vertices are given

The point of concurrence of the internal bisectors of the angles of a triangle is called the incentre and is generally denoted by I.
Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of the triangle. Let AD and BE, the bisectors of the angles A and B meet in I.

AD bisects angleBAC of triangle ABC
Hence BD/DC = AB/BC = c/b
D divides BC internally in the ratio c:b
Hence the coordinates of D are [(cx3+bx2)/(c+b), (cy3 + by2)/(c+b)]
Now, BI bisects angle ABD of triangle ABD
Hence AI/ID = AB/BD = c/BD----equation 1
But BD/DC = c/b(Proved above)
Hence BD/(BD+ DC) = c/(c+b)
BD/BC = c/(c+b)
Hence BD = ca/(c+b)(because BC = a)
From equation 1
AI/ID = c/ca/(c+b) = (c+b)/a
This shows that I divides AD internally in the ratio c+b:a
The coordinates of I are
x = {(c+b)[(cx3+bx2)/(c+b)]+ax1}/(c+b)+a = (ax1+bx2+cx3)/(a+b+c)
y = {(c+b)[(cy3+by2)/(c+b)] + ay1}/(c+b) + a = (ay1+by2+cy3)/(a+b+c)

Directions: Solve the following.
Q 1: Find the coordinates of the incentre of the triangle whose vertices are (4,-2), (-2,4) and (5,5)
5/2, 5/2

Q 2: Find the incentre of the triangle formed by (-4,1), (-1,2) and (0,5)

Question 3: This question is available to subscribers only!

Question 4: This question is available to subscribers only!

Subscription to kwizNET Learning System offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements
  • Choice of Math, English, Science, & Social Studies Curriculums
  • Excellent value for K-12 and ACT, SAT, & TOEFL Test Preparation
  • Get discount offers by sending an email to

Quiz Timer