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Question 18 (OR 2nd question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

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.

 

 

Note : This is similar to Ex 10.2, 7 of NCERT – Chapter 10 Class 10

Check the answer here https://www.teachoo.com/1833/539/Ex-10.2--7---Two-concentric-circles-are-of-radii-5-cm-and-3-cm/category/Ex-10.2/

Transcript

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
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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo