Question

given a circle with centre O, PT and PR are the tangents to the circle meeting the circle at T and R respectively. If the angle between the tangents is 35degree, then the angle between the radii OT and OR is ...................find in the blanks​

Answer 1

Answer:

145 is the angle between the radii

Answer 2

The angle between the radii OT and OR is 145°.

Step-by-step explanation:

See the attached diagram.

We have ∠ OTP = ∠ ORP = 90°

Since OT and OR are the radii of the circle with center at O. And PT and PR are the tangents to the same circle from the external point P.

Now, the quadrilateral OTPR has the summation of internal angles equal to 360°.

So, ∠ O + ∠ T + ∠ P + ∠ R = 360°

⇒ ∠ O + ∠ P = 360° - 90° - 90° = 180° {Since ∠ T = ∠ R = 90°}

Now, given that ∠ P = 35°

Hence, ∠ O = 180° - 35° = 145°

So, the angle between the radii OT and OR is 145°. (Answer)