# 5 - NCETM

```5.
AB is the diameter of the circle, centre O.
TP is a tangent to the circle at the point P.
ABT is a straight line.
P
y
T
B
x
O
A
Angle BAP = x and angle BTP = y.
Show that y = 90 – 2x.
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(Total 4 marks)
1.
Angle APB = 90
B1
or angle APB = 90
Angle PBA = 90 – x
or angle PBT = 90 + x
B1
Angle TBP = x
B1
or angle TBP = x
x + y = 90 – x
B1dep
or x + y+ 90 + x = 180
for B4 must see logical progression from x to y
[4]
```