if AP =15 cm is a tangent of circle and ABC is a secant where BC = x And AC and AP meet at A . find AC
Answers
Answer:
Here is the answer
Explanation:
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.