Question 17

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waecmaths question: 

In the diagram, PTR is a tangent to the circle centre O, if the angle TON  = 108o. Calculate the size of angle PTN

Option A: 

132o

Option B: 

126o

Option C: 

108o

Option D: 

102o

waecmaths solution: 

$\begin{align}  & \left| ON \right|=\left| OT \right|\text{    }\!\!\{\!\!\text{ Radius of a circle }\!\!\}\!\!\text{ } \\ & \angle ONT=\angle OTN\text{   }\!\!\{\!\!\text{ Base }\angle s\text{ of Isso }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \text{Let }\angle ONT=a \\ & a+a+{{108}^{\circ }}={{180}^{\circ }}\text{   }\!\!\{\!\!\text{ Sum of }\angle s\text{ in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & 2a={{72}^{\circ }} \\ & a={{36}^{\circ }} \\ & \angle ONT=\angle OTN={{36}^{\circ }} \\ & \angle OTP={{90}^{\circ }}\text{   }\!\!\{\!\!\text{ Tangent to a circle }\!\!\}\!\!\text{ } \\ & \angle PTN=\angle OTP+\angle OTN={{90}^{\circ }}+{{36}^{\circ }}={{126}^{\circ }} \\\end{align}$

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