Question

The circle below is centred at O.

AB is a tangent to this circle.
Work out the size of angle y.
Justify your answer.
O
42°
y
A
B
Not drawn accurately

Answer 1

y = 48°

Explanation:

angle A = 90°

interior angles of a triangle = 180°

therefore

y = 180 - 42 - 90

y = 48°

Answer 2

`\huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }`

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❒ Given ❒

• ➣ Mid point of a circle
• ➣ Tangent AB
• ➣ Angle "o" of 42⁰
• ➣ Angle "A" of 90⁰ (cuz it is the perpendicular of traingle given in circle)

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❒ Note ❒

• ➣here tangent AB with point O (mid point of circle) forming a traingle
• ➣we have to find "y" in the given figure (angle B)

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❒ Concept used ❒

• ➣The sum of interior angles of traingle is of 180⁰
• ➣to find the missing angle ( y ) we will use this theorem
• ➣this Concept is also know as Sum theorem

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❒ Assumption ❒

• ➣angle B = y

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❒ Let's solve ❒

`\large \pmb{➪ \: } \rm \pink{ \angle \: OAB+\angle \:ABO+\angle \:BOA = 180 \degree}`

• ➣let's substitute value now .....

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Hence the size of angle is

`\large \boxed{✥\underline{ \boxed{ \sf{y = 48 \degree \: \pmb{\green{✓}} }}}✥}`

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Hope it helps !