To draw a pair of tangents to a circle which are inclined to each other at an angle of 45- it is required to draw tangents at end points of those two radii of the circle- the angle between them should be

In quad. APBO, ∠ A = ∠ B=90^∘ nbsp; nbsp;(radius ⊥ tangent) ∠ A+ ∠ B + ∠ P +∠ O = 360 ^∘ ⇒ 90^∘ + 90^∘ + 45^∘ + ∠ 0 = 360 ^∘ ⇒ 225^∘ + ∠ 0 = 360^∘ ⇒∠ 0=36 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Tangents Drawn from an External Point

To draw a pai...

Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of $45^{\circ}$ , it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

135

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

60

No worries! We‘ve got your back. Try BYJU‘S free classes today!

90

No worries! We‘ve got your back. Try BYJU‘S free classes today!

45

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $135$

In quad. $A P B O$ ,
$∠ A = ∠ B = 90^{\circ}$ (radius $⊥$ tangent)
$∠ A + ∠ B + ∠ P + ∠ O = 360^{\circ}$
$\Rightarrow 90^{\circ} + 90^{\circ} + 45^{\circ} + ∠ 0 = 360^{\circ}$
$\Rightarrow 225^{\circ} + ∠ 0 = 360^{\circ}$
$\Rightarrow ∠ 0 = 360^{\circ} - 225^{\circ}$
$∴ ∠ 0 = 135^{\circ}$
$\Rightarrow x = 135^{\circ}$
$\Rightarrow$ Option (a).

Suggest Corrections

Join BYJU'S Learning Program

To draw a pair of tangents to a circle which are inclined to each other at an angle of 45∘, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

The correct option is A 135 In quad. APBO, ∠A=∠B=90∘ (radius ⊥ tangent) ∠A+∠B+∠P+∠O=360∘ ⇒90∘+90∘+45∘+∠0=360∘ ⇒225∘+∠0=360∘ ⇒∠0=360∘−225∘ ∴∠0=135∘ ⇒x=135∘ ⇒ Option (a).

To draw a pair of tangents to a circle which are inclined to each other at an angle of $45^{\circ}$ , it is required to draw tangents at end points of those two radii of the circle, the angle between them should be