## Book: NCERT - Mathematics

### Chapter: 12. Areas Related to Circles

#### Subject: Maths - Class 10th

##### Q. No. 8 of Exercise 12.3

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##### Fig. 12.26 depicts a racing track whose left and right ends are semicircular.The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find:(i) The distance around the track along its inner edge(ii) The area of the track.

(i) Distance around the track along its inner edge = AB + arc BEC + CD + arc DFA

= 106 + * 2πr + 106 + * 2πr

= 212 + * 2 * * 30 + * 2 * * 30

= 212 + 2 * * 30

=

= m

(ii) Area of the track = (Area of GHIJ - Area of ABCD) + (Area of semi-circle HKI - Area of semi-circle BEC) + (Area of semi-circle GLJ - Area of semi-circle AFD)

= 106 * 80 – 106 * 60 + * * (40)2 - * * (30)2 + * * (40)2 - * * (30)2

= 106 (80 – 60) + * (40)2 - * (30)2

= 106 (20) + [(40)2 – (30)2]

= 2120 + (40 – 30) (40 + 30)

= 2120 + (22/7) (10) (70)

= 2120 + 2200

= 4320 m2

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