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

Question

Philoid · Accepted 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,

PL² = PA² - AL²

⇒ PL² = 5² - 1²

⇒ PL²= 25 - 1

⇒ PL²= 24

⇒ PL = 2 √6 cm

Now,

PQ = 2 PL

⇒ PQ = 2 × 2 √6

⇒ PQ = 4 √6 cm