BDC=28 °
BD =10.02cm
Step-by-step explanation:
To solve this problem, we have to consider some basic circle theorems and their practical applications-
- Equal arc/chord subtends equal angles at the circumference.
- Diameter subtends right angle on the circumference of the circle.
By using these two theorems we proceed-
In the given figure chord BD subtends equal angles at the opposite circumference i.e. ∠BAC and ∠BDC
Therefore ∠BAC = ∠BDC=28° ∴ ∠BDC=28
°
Since diameter subtends a right angle at the circumference, ∴ ∠BCD=90
Hence, ΔBDC is a right-angled triangle with BD as the hypotenuse.
BC=4.7cm
Thus sin (∠BDC)= BC/BD (∠BDC=28 )
BD= BC/sin 28
°
Putting the values of BC and Sin 28
°
BD= 4.7/0.469=10.02 cm
