Properties of Triangles 3 Question 15

15. Circle with radii 3,4 and 5 touch each other externally, if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the point of contact.

(2005, 2M)

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Answer:

Correct Answer: 15. 5

Solution:

  1. Since, the circles with radii 3,4 and 5 touch each other externally and P is the point of intersection of tangents.

P is incentre of ΔC1C2C3.

Thus, distance of point P from the points of contact

= inradius (r) of ΔC1C2C3

i.e. r=Δs=s(sa)(sb)(sc)s

where, 2s=7+8+9s=12

Hence, r=(127)(128)(129)12=54312=5



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