Question

If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is

Answer 1

Given,

The angle between two radius of a circle is 110°

To find,

Angle between the two tangents.

Solution,

According to the attached diagram, the angle between two radius or ∠AOB = 110°.

Now, the angle between the radius and it's tangent is 90°.

Which means,  ∠OAP and  ∠OBP are 90°.

Now, we need to calculate ∠APB.

We know that the sum of the four internal angles of any four sided polygon is 360°.

In AOBP,

∠AOB + ∠OAP +  ∠OBP + ∠APB = 360°

110°+90°+90°+∠APB = 360°

290+∠APB = 360°

∠APB = 360°-290°

∠APB = 70°

Hence, the angle between two tangents is 70°.

Answer 2

Given :- If the measure of angle between two radii of a circle is 110°, then the measure of angle between tangents at the outer end of radii is …………?

Solution :-

given that,

→ ∠AOB = 110° .

→ OA = OB = radius .

we know that,

• Radius is perpendicular to the tangent at the point of contact .
• sum of interior angles of a quadrilateral is 360° .

So,

→ ∠OAC = ∠OBC = 90° .

therefore,

→ ∠AOB + ∠OAC + ∠OBC + ∠ACB = 360° .

→ 110° + 90° + 90° + ∠ACB = 360°

→ 290° + ∠ACB = 360°

→ ∠ACB = 360° - 290°

→ ∠ACB = 70° (Ans.)

Hence, the measure of angle between tangents at the outer end of radii is 70° .

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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