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Question 18
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The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find the length of AP

Last updated at Nov. 27, 2018 by Teachoo

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Question 18
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The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find the length of AP

Transcript

Question 18 The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find the length of AP Let’s first draw the figure We need to find length of AP Join OD Now, OD is the radius of smaller circle and BD is the tangent to the smaller circle So, OD ⊥ BD (Tangent is perpendicular to the radius) ∴ ∠ ODB = 90° Also, in bigger circle AB is the diameter, and point P is a point in the semi-circle of the bigger circle ∴ ∠ APB = 90° (Tangent is perpendicular to the radius) In Δ ABP and Δ OBD ∠ APB = ∠ ODB Both 90°) ∠ ABP = ∠ OBD (Common) Δ ABP ~ Δ OBD (AA Similarity) Now, sides of similar triangles are proportional 𝐴𝑃/𝑂𝐷 = 𝐴𝐵/𝑂𝐵 𝐴𝑃/8 = 26/13 (Since AB is diameter of bigger circle, AB = 2 × 13 = 26 cm) 𝐴𝑃/8 = 2 AP = 2 × 8 AP = 16 cm We need to find length of AP

CBSE Class 10 Sample Paper for 2019 Boards

Paper Summary

Question 1

Question 2 (Or 1st)

Question 2 (Or 2nd)

Question 3 (Or 1st)

Question 3 (Or 2nd)

Question 4

Question 5

Question 6

Question 7 (Or 1st)

Question 7 (Or 2nd)

Question 8 (Or 1st)

Question 8 (Or 2nd)

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16 (Or 1st)

Question 16 (Or 2nd)

Question 17 (Or 1st)

Question 17 (Or 2nd)

Question 18 You are here

Question 19 (Or 1st)

Question 19 (Or 2nd)

Question 20

Question 21 (Or 1st)

Question 21 (Or 2nd)

Question 22

Question 23 (Or 1st)

Question 23 (Or 2nd)

Question 24

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Question 26

Question 27 (Or 1st)

Question 27 (Or 2nd)

Question 28 (Or 1st)

Question 28 (Or 2nd)

Question 29

Question 30

Class 10

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.