In the figure, tangents drawn through the points
'p' and Q' of the cicle meet at "A" angleA = 40", AP=5cm
8
a) Find angle AQP
b) Find AQ
c) Calculate angleR
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Answer:
Since PB is not a tangent, PA and PB are not equal.
In ΔAPB,m∠BPA=50
o
(given)
m∠BAP=50
o
(Two angles in an isosceles triangle are equal)
So, now using angle sum property in ΔAPB, we have
m∠ABP=180
o
−(50
o
+50
o
)=80
o
In ΔABC,m∠ABC=180
o
−80
o
=100
o
m∠ACB=m∠BAP=50
o
(Each of the two angles made by a tangent to a circle and a chord through the point of contact is equal to an angle in the segment on the other side of the chord.)
Now using angle sum property in ΔACB, we have
m∠BAC=180
o
−(100
o
+50
o
)=30
o
Note: Given that ΔAPB is isosceles, but its equal sides are not given. The angles calculated above are based on the assumption that BA = BP. If we take AP = AB, it is not possible to find all the angles
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