Question

On a semicircle with diameter ad, chord bc is parallel to the diameter. Further, each of the chords ab and cd has length 2, while ad has length 8. What is the length of bc?

Answer 1

Answer:

BC = 7 cm

Step-by-step explanation:

AD = Diameter = 8 cm

=> ABD is a right angle Triangle

=> BD²  = AD² - AB²

=> BD² = 8² - 2²

=> BD = 2√15

Let Draw BP ⊥ AP

Area of ΔABD  = (1/2) * AB * BD = (1/2) * AD * BP

=> (1/2) * 2 * 2√15 = (1/2) * 8 * BP

=> BP = √15/2

Now in ΔAPB

AB² = AP² + BP²

=> 2² = AP² + (√15/2)²

=> 4 = AP² + 15/4

=> AP² = 1/4

=> AP = 1/2

Similarly DQ = 1/2  ( CQ ⊥ AD)

=> BC = AB -  AP - DQ

=> BC = 8 -1/2 - 1/2

=> BC = 7 cm