26) In given figure, find the actual length of AB, OB and OA. (centre of the circle is O)
where AB = x + 1 cm, AO = x + 2 cm and OB = x-6 cm
Answers
Answer:
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Step-by-step explanation:
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Given : AB = x + 1 cm, AO = x + 2 cm and OB = x-6 cm
O is center of circle AB is Tangent
To Find : the actual length of AB, OB and OA
Solution:
AB is tangent Hence AB ⊥ OB
=> ΔABO is right angle triangle
AO is hypotenuse
OB & AB are perpendicular sides
Applying Pythagoras theorem :
AO² = AB² + OB²
=> (x + 2)² = (x + 1)² + (x - 6)²
=> x² + 4x + 4 = x² + 2x + 1 + x² -12x + 36
=> x² -14x + 33 = 0
=> x² - 11x - 3x + 33 = 0
=> (x - 11)(x - 3) = 0
=> x = 11 , 3
3 not possible as then OB = 3 - 6 is - 3 and not possible
AB = 11 + 1 = 12 cm
AO = 11+ 2 = 13 cm
OB = 11 - 6 = 5 cm
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