In the figure,two circles with centres A and B of 5 cm and 3 cm touch other internally If the - Maths - Circles

Question

In the figure,two circles with centres A and B of 5 cm and 3 cm
touch other internally If the perpendicular bisector of segment AB
meets the bigger circle in P and Q Find the length of PQ

ramandeep.singh · Accepted Answer

$r_{1} = 5 c m r_{2} = 3 c m$

As the 2 circles touch internally,

∴AB = r₁ - r₂ = 2 cm

Also, PQ is the perpendicular bisector of AB.

∴AC = BC = 1 cm

In right ΔACP,

AP² = AC² + CP²

⇒5² = 1² + CP²

⇒CP² = 24

⇒CP = 2√6 cm

Hence, PQ = 2CP

= 4√6 cm

1

In the figure,two circles with centres A and B of 5 cm and 3 cm touch other internally.If the perpendicular bisector of segment AB meets the bigger circle in P and Q.Find the length of PQ.