Question 72

Two circles of diameters 4.8 cm and 8 cm are such that the distance betweentheir centres is 6.5 cm. What is the length of a common tangent to the circles that does notintersect the line joining the centres ?

Solution

Given that AB = 6.5 cm, CD= 6.5 cm, BC= 2.4, AP = 4 cm and PC is common tangent

PD = PA - AD = 4-2.4= 1.6 cm

By Pythagoras theorem, In triangle PDC angle P = 90 degree

$$PC^2=CD^2-PD^2$$

$$PC^2=6.5^2-1.6^2=39.69$$

PC = 6.3 cm

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