Question

draw circle of radius 4 cm draw two tangents to the circle inclined at an angle of 60 degree to each other

do the construction as per question and write the steps of constructio​

Answer 1

Answer:

refer to the attachment

50 points answerer

Answer 2

First see the circle above ☝︎☝︎☝︎☝︎☝︎

Now,

The tangents can be constructed in the following manner:

Step 1 :-

Draw a circle of radius 4 cm and with centre as O.

Step 2 :-

Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A.

Step 3 :-

Draw a radius OB, making an angle of 120° (180° − 60°) with OA.

Step 4 :-

Draw a perpendicular to OB at point B. Let both the perpendiculars intersect at point P. PA and PB are the required tangents at an angle of 60°.

Justification :-

The construction can be justified by proving that ∠APB = 60°

By our construction :-

∠OAP = 90°

∠OBP = 90°

And ∠AOB = 120°

We know that the sum of all interior angles of a quadrilateral = 360°

∠OAP + ∠AOB + ∠OBP + ∠APB = 360°

90° + 120° + 90° + ∠APB = 360°

∠APB = 60°

This justifies the construction.

Hope it helps !