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Ex 10.4, 1 - Two circles of radii 5 cm and 3 cm intersect - Equal chords and their distance from centre

Ex 10.4, 1 - Chapter 10 Class 9 Circles - Part 2
Ex 10.4, 1 - Chapter 10 Class 9 Circles - Part 3 Ex 10.4, 1 - Chapter 10 Class 9 Circles - Part 4 Ex 10.4, 1 - Chapter 10 Class 9 Circles - Part 5 Ex 10.4, 1 - Chapter 10 Class 9 Circles - Part 6

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Ex 10.4, 1 Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord. Given: Circle C1 with radii 5cm & C2 with radii 3cm Intersecting at P & Q. OP = 5cm , XP = 3cm & OX = 4cm To find: Length of common chord i.e., length of PQ Solution: Let the point where OX intersects PQ be R. In Δ POX & Δ QOX OP = OQ XP = XQ OX = OX ∴ Δ POX ≅ Δ QOX ∠ POX = ∠ QOX Also, In Δ POR & Δ QOR OP = OQ ∠ POR = ∠ QOR OR = OR ∴ Δ POR ≅ Δ QOR ⇒ ∠ PRO = ∠ QRO & PR = RQ Since PQ is a line ∠ PRO + ∠ QRO = 180° ∠ PRO + ∠ PRO = 180° 2∠ PRO = 180° ∠ PRO = (180°)/2 ∠ PRO = 90° Therefore, ∠ QRO = ∠ PRO = 90° Also, ∠ PRX = ∠ QRO = 90° Let OR = x, So, XR = OX – OR = 4 – x Now, From (4) & (5) 52 – x2 = –7 – x2 + 8x 25 – x2 = –7 – x2 + 8x 25 + 7 – x2 + x2 = 8x 32 = 8x 8x = 32 x = 32/8 x = 4 Putting value of x in (4) PR2 = 25 – x2 PR2 = 25 – 42 PR2 = 25 – 16 PR2 = 9 PR = √9 = 3 ∴ PQ = 2PR = 2 × 3 = 6 Hence, length of common chord = 6 m Note: OR = x = 4 cm & XR = 4 – x = 4 – 4 = 0 cm since XR = 0 this means point X & R coincide Hence actual figure is as follows

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.