Question

1) 4cm ತ್ರಿಜ್ಯ ಇರುವ ವೃತ್ತಕ್ಕೆ ಸ್ಪರ್ಶಕ ಗಳ ನಡುವಿನ ಕೋನವು 60° ಆಗುವಂತೆ ಎರಡು ಸ್ಪರ್ಶಕಗಳನ್ನು ರಚಿಸಿ,​

Answer 1

Question :- For a circle with a radius of 4cm, create two tangents so that the angle between the tangents is 60° ?

Solution :- (Refer to image.)

Steps of construction :-

Step 1) :- First draw a circle of radius 4 cm and with centre O.

Step 2) :- Now, let us take two points A and B on the circumference of the circle and join OA and OB. OA and OB are the radius of the circle .

Step 3) :- Now, we have to make sure angle between AO and OB , at the centre O is equal to 120° .

Step 4) :- Now from points A and B draw perpendiculars such that, both perpendiculars intersect at point C.

we get,

• PA and PB are the tangents to the circle.

now, in quadrilateral OBCA ,

→ ∠BOA + ∠OBC + ∠OAC + ∠BCA = 360° (Angle Sum Property.)

→ 120° + 90° + 90° + ∠BCA = 360°

→ 300° + ∠BCA = 360°

→ ∠BCA = 360° - 300°

→ ∠BCA = 60° .

therefore, we can conclude that, the angle between the tangents PA and PB is equal to 60° .

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Answer 2

please color the picture