Question

PQ &ST are the two chords of a circle with centre O such that PQ =24cm &ST =10 cm & PQ || ST . determine the radius of circle if they are on (i) opposite side of the centre &dist between them is 17 cm (ii) same side of centre and distance between them is 7cm​

Answer 1

Answer:

: Given AB and CD are two chords of a circles D and E are midpoints of AB ,CD respectively. CD = DB = 12 cm and AE = EB = 5 cm Distance between two chords = 17 cm Distance between O and F = x cm Distance between O and E = (17- x) cm In a ΔOEB is an right angle traingle then OB2 = OF2 + FD2 = (17- x)2 + 52 ----------→(1) In a ΔOFD is an right angle traingle then OD2 = OE2 + EB2 = (x)2 + 122 ----------→(2) But OB = OD ( radius ) From 1 & 2 (17- x)2 + 52 = (x)2 + 122 ⇒ 289 + x2 -34x +25 = x2 +144 ⇒ 34x = 170 ∴ x = 5 subsitute x in (1 ) 0r (2) equations ∴ radius of the circle = 13.

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