Question
Three-quarters of a circle is shown in the figure; OA and OB are two radii perpendicular to each other. C is a point on the circle. What is angle ACB?
The correct answer is
$45^\circ$
To find the angle ∠ACB, we need to analyze the given geometry of the circle.
Let's consider the properties of circles and triangles:
- OA and OB are radii of the circle and are perpendicular to each other, hence ∠AOB = 90°.
- Since OC is also a radius of the circle, triangle OAC is an isosceles right triangle, making ∠OAC = ∠OCA = 45°.
- Similarly, ∠OCB will also create an isosceles right triangle since OB = OC.
- Therefore, triangle OCB is also an isosceles right triangle, making ∠OCB = 45°.
Since angle ∠AOB = 90°, the external angle ∠ACB of triangle OCB is calculated as:
\(∠ACB = 180° - ∠OCA - ∠OCB = 180° - 45° - 90° = 45°.\)
Thus, the correct answer is 45°.
Was this answer helpful?
Important Questions from Geometry (Notes)
- A 6 cm long chord of a circle is at a distance of 4 cm from the centre of the circle. Find the distance of 8 cm long chord of the same circle from the centre.
- In a triangle PQR, if $\angle P + \angle R = 150^\circ$ and $\angle P + 3\angle Q = 170^\circ$, then $\angle P$ is equal to :
- PQR is a triangle. The bisectors of the internal angle $\angle Q$ and external angle $\angle R$ intersect at M. If $\angle QMR = 40^\circ$, then $\angle P$ is :
- A $2\text{ m}$ long ladder is to reach a wall of height $1.75\text{ m}$. The largest possible horizontal distance of the ladder from the wall could be
In the context of tiling a plane surface, which of the following polygons is the odd one out?
Need Expert Advice?
