Question

We have two circles (A; 3cm) and (B; 2cm) intersecting at C, D. AB = 4cm. The circles with center A, B intersect segment AB at K, I. respectively. a, Calculate CA, CB, DA, DB. b, Is I the midpoint of segment AB? c, Calculate IK.

Answer 1

REPLY: a) (A; 3cm) and (B; 2cm) intersect at C; D should: + C, D lie on the circle (A; 3cm), deduce AC = AD = 3cm. + C, D lie on the circle (B; 2cm), deduce BC = BD = 2cm. b) A circle (B; 2cm) cuts section AB at I should: + I lie on the circle (B; 2cm), deduce BI = 2cm. + I is on line AB, deduce IA + IB = AB. Where BI = 2cm; AB = 4cm so AI = 2cm. Hence BI = AI. Combined with I on the line AB deduce I is the midpoint AB. c) The circle (A; 3cm) cuts section AB at K so K belongs to the circle (A; 3cm), deducing AK = 3cm. On the line AB has AI <AK so I is between A and K. Hence AI + IK = AK. Which AK = 3cm; AI = 2cm so IK = 1cm

Answer 2

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