Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

Two circles of radii 10 cm and 17 cm intersect at two points and the distance between their centres is 21 cm. Find the length of the common chord.
Asked by | 30 Jan, 2012, 08:54: PM
Expert Answer
Let the radius of the circle centred at O and O' be 17 cm and 10 cm respectively. OA = OB = 17 cm O'A = O'B = 10 cm OO' will be the perpendicular bisector of chord AB. ? AC = CB It is given that, OO' = 21 cm Let OC be x. Therefore, O'C will be 21 ? x. In ?OAC, OA2 = AC2 + OC2 ? 172 = AC2 + x2 ? 289  x2 = AC2 ... (1) In ?O'AC, O'A2 = AC2 + O'C2 ? 102 = AC2 + (21 ? x)2 ? 100 = AC2 + 441 + x2 ? 42x ? AC2 = ? x2 - 341 + 42x ... (2) From equations (1) and (2), we obtain 289? x2 = ? x2 ? 341 + 42x 42x = 630 x = 15 Now, AC2 = 289  x2 = 289 ? 152 = 289 ? 225 = 64 ? AC = 64 cm Length of the common chord AB = 2 AC = (2 × 64) cm = 128 cm
Answered by | 31 Jan, 2012, 09:55: AM

Concept Videos

CBSE 9 - Maths
Asked by indu.suresh1220 | 27 Dec, 2023, 11:12: PM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by subbusuchi1978 | 05 Nov, 2023, 10:24: AM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by rameshsonkar1234ramesh | 21 Dec, 2022, 11:03: PM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by sdmbotch1123 | 17 Dec, 2022, 09:39: PM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by geetaradha8835 | 16 Dec, 2022, 07:59: PM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by rairai4971 | 11 Jun, 2022, 09:03: AM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by chalkekalyani80 | 06 Mar, 2022, 11:25: AM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by sangeetabharti123456789 | 22 Feb, 2022, 09:01: AM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by manognareddy.p28 | 25 Jul, 2021, 12:52: PM
ANSWERED BY EXPERT
CBSE 9 - Maths
Asked by Samidhaindulkar133 | 11 Mar, 2021, 04:03: PM
ANSWERED BY EXPERT