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Question 19. In the given figure, AD is a diameter of a circle with centre O and AB is tangent at A. C is a point on the circle such that DC produced intersects the tangent of B. If ∠ABC = 50°, find ∠AOC.

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One of the most important and exam oriented question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

It is given that AD is a diameter of a circle with centre O and AB is tangent at A.

C is a point on the circle such that DC produced intersects the tangent of B.

Also ∠ABC = 50°,  now we have to find ∠AOC.
ICSE Avichal publication
Understanding ICSE Mathematics
Question 19

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  1. Solution:
    Given AB is tangent to the circle at A and OA is radius, OA ⊥ AB
    In ∆ABD
    <DAB+<ABD+<ADB=180

    90+50+<ADB=180

    <ADB=40

    <AOC=<OCD+<ODC=40+40=80

     

     

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