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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deepaksoniGuru

Asked: April 15, 20212021-04-15T09:11:41+05:30 2021-04-15T09:11:41+05:30In: ICSE

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.
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Understanding ICSE Mathematics
Question 19

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AAREKH · Answer 1 · 2021-04-17T13:09:24+05:30

AAREKH Guru

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