O is the centre of circle having radius 5cm. OM perpendicular on chord AB. If OM is 4 cm, then the length of chord AB is
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Answered by
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the diagram is bad but understand...
5 cm is radius so that becomes hypotenuse of OAM.
So, OM - 4cm OA-5 cm
OA²=OM² + AM² (Pythagoras Theorem)
5² = 4² + AM²
25 = 16 + AM²
25 - 16 = AM²
9 = AM²
√9 = AM
3 = AM.
Now AM = BM since the two s are congruent. OM is common side, OA = OB = Radius of circle.
So, AM=BM=3cm
so AB = AM + BM = 3+3 = 6cm.
5 cm is radius so that becomes hypotenuse of OAM.
So, OM - 4cm OA-5 cm
OA²=OM² + AM² (Pythagoras Theorem)
5² = 4² + AM²
25 = 16 + AM²
25 - 16 = AM²
9 = AM²
√9 = AM
3 = AM.
Now AM = BM since the two s are congruent. OM is common side, OA = OB = Radius of circle.
So, AM=BM=3cm
so AB = AM + BM = 3+3 = 6cm.
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