Question

QUESTION--: What should be the angle between the two tangents which is drawn at the end of two radii and are inclined at an angle of 45 degrees?
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Answer 1

Step-by-step explanation:

PA and PB are tangents drawn from an external point P to the circle.

∠OAP=∠OBP=90 ∘

(Radius is perpendicular to the tangent at point of contact)

In quadrilateral OAPB,

∠APB+∠OAB+∠AOB+∠OBP=360∘

45∘ +90 ∘ +∠AOB+90° =360∘

225∘ +∠AOB = 360∘

∠AOB=360∘–225∘ =135 ∘

Thus, the angle between the two radii, OA and OB is 135 ∘

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Answer 2

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Let PA and PB be the desired tangents to a circle with centre O from an exterior point P

Then,

∠APB = 45°

BOAB must be a cyclic quadrilateral.

∠AOB + ∠APB = 180° = ∠AOB

So, the angle between the two radii must be 135°