Two circles touches internally. The sum of their areas is 170π cm2 and between distance between their centres is 4 cm find radii
Answers
Answer:
best of luck for exam
Step-by-step explanation:
Two circle touch internally. The sum of there areas is 170 πcm
2
and the distance between their centres is 4 cm. Find the radii of the circles
question
December 20, 2019
avatar
Tanveer Devgharkar
Share
Save
ANSWER
Let radius of circle A be r
1
and radius of circle B be r
2
Given, r
1
−r
2
=4 ---------(i)
and πr
1
2
+πr
2
2
=170π
⇒r
1
2
+r
2
2
=170 -----------(ii)
(i) r
1
=4+r
2
Now, putting this value in (ii), we get
⇒(4+r
2
)
2
+r
2
2
=170
⇒16+8r
2
+r
2
2
+r
2
2
=170
⇒2r
2
2
+8r
2
−154=0
⇒2r
2
2
+22r
2
−14r
2
−154=0
⇒2r
2
(r
2
+11)−14(r
2
+11)=0
⇒(r
2
+11)((2r
2
−14))=0
⇒r
2
=−11 (not possible) or r
2
=7
Thus, r
2
=7
r
1
=r
2
+4
⇒r
1
=7+4=11
Thus, the radius of the two circles are 11 cm and 7 cm.
Answer:
radii of two circles is 11 cm and 7 cm