Question

Challenge for all MODs and STARs.


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Answer 1

Given : A circle of Radius 10 cm

To Find : length of AC

Solution:

Extend  BD to meet Circle at E

DE = 2x

BD * DE  = AD * DC

=> 4 * 2x = AD * 2

=> AD = 4x

AC = AD + CD =4x + 2

BE = 4 + 2x

Let say O is center and OM ⊥ BE

OB = OE = Radius = 10

BM  = EM = (4 + 2x)/2 = 2 + x

OM² = OB² - BM²  

=> OM² = 10² - (x   + 2)²

=> OM²  = 100 - x²   - 4  - 4x

=> OM²  = 96 - x²    - 4x

OM + 2  =  AC/2

=> OM + 2 = 2x + 1

=> OM = 2x - 1

=> OM²  = 4x² - 4x + 1

4x² - 4x + 1 =  96 - x²    - 4x

=> 5x² = 95

=>  x² = 19

=> x  =  √19

AC =  4x + 2  

=   4√19 + 2

= 19.4356 cm

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