Question
Download Solution PDFTwo circles are having radii 9 cm and 12 cm and intersect each other. The distance between their centres is 15 cm. What is the length (in cm) of their common chord?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe line joining the centre will be perpendicular to the common chord and will bisect it.
In ΔNPR and ΔNQR
NP = NQ (radii)
NR is common
∠PNR = ∠QNR [∵ NP and NQ are tangents to the larger circle]
∴ The triangles are congruent
ΔMNP is a right angled triangle. Because the sides are Pythagorean triplet i.e. 122 + 92 = 152
Area of ΔMNP = 1/2 × MN × PR = 1/2 × MP × NP
⇒ MN × PR = MP × NP
⇒ 15 × PR = 12 × 9
PR = 7.2 cm
PQ = 2 × PR = 14.4 cm
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