Circle Angle Theorem Explanation
The question relates the angle subtended by an arc at the center of a circle to the angle subtended by the same arc at any point on the circumference. The key theorem states that the angle at the center is double the angle at the circumference.
Applying the Circle Theorem
We are given:
- Points A, B, and C lie on a circle with center O.
- The angle at the circumference, $\angle \text{ACB} = 47.5^{\circ}$.
- We need to find the angle at the center, $\angle \text{AOB}$, on the minor arc $\widehat{\text{AB}}$.
Calculating Angle AOB
According to the circle theorem:
$\angle \text{AOB} = 2 \times \angle \text{ACB}$
Substitute the given value:
$\angle \text{AOB} = 2 \times 47.5^{\circ}$
$\angle \text{AOB} = 95^{\circ}$
Conclusion
The angle $\angle \text{AOB}$ on the minor $\widehat{\text{AB}}$ is $95^{\circ}$.
Similar Questions
- PQ is a diameter of a circle whose centre is O. If a point R lies on the circle and $\angle RPO$ is $39^\circ$, then find the measure of $\angle RQP$.
- $1^{\circ}$ of latitude is equal to ___ km approximately.
- A wheel makes 1000 revolutions in covering a distance of 154 km. Find the radius (in metre) of the wheel.
- Two intersecting circles are said to be orthogonal if the angle between them is a/an _____.
A circle having centre $c_1$, radius $r_1$ = 5 cm is placed against a right angle. Another smaller circle having centre $c_2$, radius $r_2$ is also placed touching the sides of angle and the bigger circle as shown in the figure. Find the radius, $r_2$ in cm, of the smaller circle.
In the given circle with centre O, the obtuse angle at the centre measures $104^\circ$. In the quadrilateral drawn inside the circle, what is the measure of the angle opposite to $\angle\text{O}$? [Figure is not drawn to scale.]
- The chord of contact of tangents drawn from a point on the circle $x^2 + y^2 = a^2$ to the circle $x^2 + y^2 = b^2$ touches the circle $x^2 + y^2 = c^2$ such that $b^m = a^n c^p$, where $m,n,p \in \mathbb{N}$. Find the value of $m + n + p + 10$.
- Find the length of the tangent from any point on the circle $x^2 + y^2 + 2011x + 2012y + 2013 = 0$ to the circle $x^2 + y^2 + 2011x + 2012y + 2014 = 0$.
- If a point (1, 2) is translated 2 units through the positive direction of x-axis and then the tangents drawn from that point to the circle $x^2 + y^2 = 9$, find the angle between the tangents.
- The angle of a sector is 30°. If its radius is 42 cm then the length of the arc of the sector is:
Important Questions from Circles
If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
What is the area of minor segment ?
What is the area of major segment ?
A straight line x = y + 2 touches the circle 4(x 2+ y 2) = r 2. The value of r is
If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are
