Question

The figure below shows two circles of radii 10.5 and 8.4cm and with centres A and B respectively. The common chord PQ 9cm.

1. Calculate angle PAQ. 
2. Calculate angle PBQ. 
3. Calculate the area of the shaded part. 

Answer 1

Calculate angle PAQ.

 < PAQ = <PAM + <QAM
< PAM = sinθ1 =^4.5/_10.5=0.4286
Sin ^-1 (0.4286) = 25.38º
< QAM = <PAM = 25.38º
→<LAP = 25.38x2= 50.76º

Calculate angle PBQ. 
<PBQ = < PBM + <QBM
< PBM = sin∝1 =⁴⁵/₈₄=0.5357
Sin-1 (0.5357) = 32.39º
< PBM = <QBM = 32.39º
<PBQ = 32.390x 2 = 64.78º
 

Calculate the area of the shaded part. 

area of segment = area of a section – area of D

Taking (i)
=
= 48.84 – 42.69 = 6.15cm²
Taking (ii)
=
= 39.89 – 31.92 = 7.97cm²
= (6.15 + 7.97) cm² = 14.12cm²