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Standard IX

Mathematics

SSS, SAS, AAS, ASA, RHS Criteria for Congruency of Triangles

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

(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
Also, AP²= BP²+ AB²
Or BP²= AP² - AB²
Or BP²= 5² - 4²
Or BP = 3 cm
∴ ΔABP is a right angled and PQ = 2 × BP = (2 × 3) cm = 6 cm

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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

(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 Also, AP2 = BP2 + AB2 Or BP2 = AP2 - AB2 Or BP2 = 52 - 42 Or BP = 3 cm ∴ ΔABP is a right angled and PQ = 2 × BP = (2 × 3) cm = 6 cm

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

(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
Also, AP²= BP²+ AB²
Or BP²= AP² - AB²
Or BP²= 5² - 4²
Or BP = 3 cm
∴ ΔABP is a right angled and PQ = 2 × BP = (2 × 3) cm = 6 cm