(2) In the figure, the circles with centres A and B
touch each other at E. Line I is a common
tangent which touches the circle at C and D
respectively. Find the length of seg CD if the
radii of the circle are 5 cm and 8 cm.
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Answer:
If two circles touch each other externally, then distance between their centres is equal to the sum of their radii.
∴ AB = AE + EB = 4 cm + 6 cm = 10 cm
It is given that l is a common tangent which
∴ ∠ACD = ∠BDC = 90º (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)
Draw AF ⊥ BD.
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