Question

Draw a pair of tangents to a circle of radius 3cm which are inclined to each other at an angle of 80°​

Answer 1

Step-by-step explanation:

Steps of Construction:

Step I: Draw a circle with centre O and radius 3 cm.

Step II: Draw any diameter AOB.

Step III: Draw a radius OC such that ∠ BOC = 80°.

Step IV: At C, we draw CM ⊥ OC and at A, we draw AN ⊥ OA.

Step V: Let the two perpendiculars intersect each other at P. Then, PA and PC are required tangents.

Justification: Since OA is the radius, so PA has to be a tangent to the circle. Similarly, PC is also tangent to the circle.

∠APC = 360° – (∠OAP + ∠OCP + ∠AOC)

= 360° – (90° + 90° + 100°) = 360° – 280° = 80° Hence, tangents PA and PC are inclined to each other at an angle of 80°.

Answer 2

Answer:

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Step-by-step explanation:

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