CBSE Class 10 Maths (Standard) 2024 · Paper 30/1/1 · Question 38

Circles 4 marks Medium

A backyard is in the shape of a triangle

A B C

with right angle at

B

A B = 7

m and

B C = 15

m. A circular pit was dug inside it such that it touches the walls

A C

B C

and

A B

P

Q

and

R

respectively such that

A P = x

m. Based on the above information, answer the following questions :

Right triangle ABC with inscribed circle touching at P, Q, R

iFind the length of $A R$ in terms of $x$ .[1]
iiWrite the type of quadrilateral $B QO R$ .[1]
iii (a)Find the length $P C$ in terms of $x$ and hence find the value of $x$ .[2]
iii (b)[OR] Find $x$ and hence find the radius $r$ of circle.[2]

Answer

(i)

A R = x

m; (ii)

B QO R

is a square; (iii)(a)

P C = (8 + x)

m and

x = \frac{274 - 8}{2} \approx 4.28

m; (iii)(b)

x \approx 4.28

m and

r = 7 - x = \frac{22 - 274}{2} \approx 2.72

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