Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

In the given figure, PA and PB are tangents to a circle centred at O. If
ZAPB = 30°, then OAB equals:-
​

Sagot :

nengikim

Answer:

Consider the triangle formed by points O, A, and P. Since OA and OP are radii of the circle centered at O, they are congruent. This makes triangle OAP isosceles, and since PA is tangent to the circle at A, angle OAP = 90 degrees.

Using the angle sum property in triangle OAP, we get:

∠OAP + ∠OAB + ∠PAB = 180°

Substituting 90° for ∠OAP and noting that angles at the points of tangency (like ∠PAB) are congruent, we get:

90° + ∠OAB + ∠PAB = 180°

Since we are given that ∠APB = 30°, we can replace ∠PAB with 30° in the equation.

90° + ∠OAB + 30° = 180°

Combining like terms, we get:

∠OAB + 120° = 180°

Subtracting 120° from both sides isolates ∠OAB:

∠OAB = 180° - 120°

Therefore, ∠OAB = 60°.

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.