In the given figure Two circles pass
through each other centres if AB=6cm
then find radius of incircle of triangle
ABC?
Answers
Answer:
MATHS
In the figure triangle ABC is inscribed in a circle with cen-tre O. If CA=CB=15cm and AB=6cm, find the radius of the circle.
559589
Share
Study later
ANSWER
Let D be the midpoint of AB, and let CD produced meet the circle in E.
Join AE.
Let CD=h,DE=x,AE=l.
We have AC=BC=15,AD=3.
∵CD is the perpendicular bisector of AB, CD passes through the centre O of the circle.
∴CE is a diameter of the circle
∴∠CAE=90
o
....... (angle in a semi circle is a right angle)
From the right-angled ΔADC,
h
2
=AC
2
−AD
2
=15
2
−3
2
=225−9=216
∴h=
216
=6
6
.
From the right-angled ΔCAE, we have
(h+x)
2
=CA
2
+AE
2
=15
2
+l
2
=15
2
+3
2
+x
2
.
∴h
2
+x
2
+2hx=225+9+x
2
.
⟹216+2hx=234;
⟹2hx=18
⟹x=
2h
18
=
6
6
9
=
2
6
3
.
Therefore, diameter CE=h+x=6
6
+
2
6
3
=
2
6
72+3
=
2
6
75
.
So, radius of the circle=
2
diameter
=
4
6
75
cm.
How satisfied are you with the answer?
This will help us to improve better
ASK
Get Instant Solutions, 24x7
No Signup required
girl
Prev Question
Next Question
Practice important Questions
Class 9 Maths Chapter 4 Unit 4
42 Qs
Related Questions to study
Given two secants, solve for x.
Study later
View Answer
Two chords AB and CD intersect at a point P within a circle.
If AP=4 cm,CP=3 cm,PD=8 cm, find PB.
Study later
View Answer
VIEW MORE
20,000+
Learning videos
8,000+
Fun stories
10,000+
Fundamental concepts
8,00,000+
Homework Questions
BROWSE BY
ClassesBoardsExams
MODULES
Online ClassesMock TestsAdaptive PracticeLive Doubts
Stay upto date with our Newsletter!
Stay informed, stay ahead. Be a topper
Your email address
About Us
Brand Resources
Press
Customer Stories
Jobs
Educators
Fellowship
Learning Planet
Guides
Ask
Blog
Bytes
News
Terms of Service
Privacy Policy
Contact Us
FAQs
Google Play
App Store
IN
India
Add to home screen
Add
Downloading the app is too much, right? Add Toppr Answr to your homescreen