Q. 154.6( 18 Votes )

# In the adjoining figure, two circles with centers at and and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of meets the bigger circle in and find the length of

Answer :

Join AP.

Let PQ intersect AB at L,

Then, AB = 5 – 3 = 2 cm

PQ is the perpendicular bisector of AB,

Then,

AL = (1/2) AB

⇒ AL = (1/2) 2 = 1 cm

In triangle APL,

PL^{2} = PA^{2} - AL^{2}

⇒ PL^{2} = 5^{2} - 1^{2}

⇒ PL^{2}= 25 - 1

⇒ PL^{2}= 24

⇒ PL = 2 √6 cm

Now,

PQ = 2 PL

⇒ PQ = 2 × 2 √6

⇒ PQ = 4 √6 cm

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