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Question

PAQ is a tangent to the circle with center O at a point A as shown in figure. If OBA=35, find the value of BAQ and ACB. [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

OB = OA (radius)

OBA=OAB=35

From OAB,OBA+OAB+AOB=180

35+35+AOB=180

AOB=110

But ACB=12 AOB

ACB=12 (110)

ACB=55

As the tangent at any point of a circle is perpendicular to the radius through the point of contact,

OAQ=90

BAQ=OAQOAB

BAQ=9035

BAQ=55

Therefore ACB=55 and BAQ=55


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