Two tangents PA and PB to a circle with centre o are
inclined to each other at an angle of 70° then angle OAB is how much ?
Answer will be 35° according to book, but how it's not given
Answers
Question 3.
In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70°, then calculate ∠TPQuestion (2011OD)
Important Questions for Class 10 Maths Chapter 10 Circles 5
Solution:
Important Questions for Class 10 Maths Chapter 10 Circles 6
∠1 = ∠2
∠1 + ∠2 + 70° = 180°
∠1 + ∠1 = 180° – 70°
2∠1 = 110° ⇒ ∠1 = 55°
∠1 + ∠TPQ = 90°
55° + ∠TPQ = 90°
⇒ ∠TPQ = 90° – 55° = 35°
If the angle between two tangents PA and PB is 70°, then the angle subtended by the arc AB at the center of the circle (angle OAB) would be x/2 = 70°/2 = 35°.
The relationship between the angle between two tangents drawn to a circle from a point outside the circle and the angle subtended by the arc between the two points of tangency at the center of the circle can be established using geometry.
When two tangents PA and PB are drawn from a point outside the circle to the circle, they intersect at the point of tangency.
The angle between the two tangents is denoted by x.
According to the geometry of circles, the angle between the two tangents is equal to twice the angle subtended by the arc between the two points of tangency at the center of the circle. In other words, the angle subtended by the arc AB at the center of the circle (angle OAB) is equal to x/2.
This relationship can be established through geometric constructions and proofs and has various applications in engineering, surveying, and other fields where circles and arcs are used. The concept of the angle between two tangents and the angle subtended by the arc at the center of the circle is a fundamental aspect of geometry and is important for students to understand in order to have a strong foundation in the subject.
For more such questions on Tangents: https://brainly.in/question/45207599
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