Question

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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IA
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Answer 1

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