8.2 Angle between Tangent and Chord (Example 3 & 4)


Example 3:
In the diagram, PQR is a tangent to the circle QSTU at Q.


Find the values of
(a) x   (b) y
 
Solution:
(a)
UTS + ∠UQS = 180o ←(opposite angle in cyclic quadrilateral QSTU)
105o + ∠ UQS = 180o
UQS = 75o
x+ 75o + 20o = 180o(the sum of angles on a straight line PQR = 180o)
x+ 95o = 180o
= 85o
 
(b) 
PQU = ∠ QSU  ← (angle in alternate segment)
85o = 35o + y
y = 50o



Example 4:

In the diagram, ABC is a tangent to the circle BDE with centre O, at B.
Find the value of x.
 
Solution:


BED=CBD=54BDE=180542=63Isosceles triangleEBD=EDBABE=BDE=63InABE,x+45+63=180x+108=180x=72