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Standard IX

Mathematics

Perpendicular from the Center to a Chord Bisects the Chord

In the given ...

Question

In the given figure, A and B are the centres 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

(a) 3 cm

(b) 6 cm

(c) 7.5 cm

(d) 9 cm

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Solution

ANSWER:
(b) 6 cm
We know that the line joining their centres is the perpendicular bisector of the common chord.
Join AP.
Then AP = 5 cm; AB = 4 cm

PQ=6

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In the given figure, A and B are the centres 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 (a) 3 cm (b) 6 cm (c) 7.5 cm (d) 9 cm

ANSWER: (b) 6 cm We know that the line joining their centres is the perpendicular bisector of the common chord. Join AP. Then AP = 5 cm; AB = 4 cm PQ=6

In the given figure, A and B are the centres 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

(a) 3 cm

(b) 6 cm

(c) 7.5 cm

(d) 9 cm

ANSWER:
(b) 6 cm
We know that the line joining their centres is the perpendicular bisector of the common chord.
Join AP.
Then AP = 5 cm; AB = 4 cm

PQ=6