Question 18 (OR 2nd question) If the radii of two concentric circles are 4 cm and 5 cm, then find the length of each chord of one circle which is tangent to the other circle.
Given two concentric circles of radius 4 cm and 5 cm
Let AB be chord of larger circle
which is tangent to smaller circle at point P
We need to find length of chord AB
Joining OA, OB and OP
OA = OB = Radius of larger circle = 5 cm
OP = Radius of smaller circle = 4 cm
Now,
Since AB is tangent to smaller circle
∴ OP ⊥ AB
∴ ∠ OPA = ∠ OPB = 90°
Now, we use Pythagoras theorem in
both Δ OPB and Δ OPA
Using Pythagoras theorem
(Hypotenuse)2 = (Height)2 + (Base)2
In right triangle OAP
OA2 = OP2 + AP2
52 = 42 + AP2
25 = 16 + AP2
25 – 16 = AP2
AP2 = 9
AP2 = 32
AP = 3 cm
In right triangle OPB
OB2 = OP2 + BP2
52 = 42 + BP2
25 = 16 + BP2
25 – 16 = BP2
BP2 = 9
BP2 = 32
BP = 3 cm
Hence,
AB = AP + PB
= 3 + 3
= 6 cm

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.