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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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