Question 18 - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at Oct. 1, 2019 by Teachoo

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

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

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.