In the given figure, A and B are the centers of two circles having radii 5 cm and 3 cm respectively and intersecting at points P and Q respectively. If AB = 4 cm, then the length of common chord PQ is

Question

Philoid · Accepted Answer

Given: two circles having radii 6 cm and 3 cm

Construction: join AP

Consider ΔABP

Here,

AP² = AB² + BP²

5² = 4² + 3²

25 = 16 + 9

25 = 25

∴ ΔABP is right angled triangle

PQ = 2×BP

PQ = 2×3 = 6cm

∴PQ = 6cm