1) Find the value of CD in terms of x, in the adjoining figure, where O is the centre of semicircle.

2) In the given figure (circle), PT = 5, PD = 7 and PA = 2, then the value of PB - PC = ?

Dear student

Clearly,OA=OB   raduis of circleOA=OC+BCOA+OC=OC+BC+OC     Adding OC both sidesx=2OC+1OC=x-12    ...(1)So, OB=OC+BC=x-12+1=x+12Also, OD=OB=x+12    [radius]Now, In OCD,by pythagoras theoremCD2=OD2-OC2CD2=x+122-x-122CD2=x+12+x-12x+12-x-12CD2=xSo, CD=x
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