Advertisements
Advertisements
Question
In the following figure, if ∠OAB = 40º, then ∠ACB is equal to ______.
Options
50º
40º
60º
70°
Advertisements
Solution
In the following figure, if ∠OAB = 40º, then ∠ACB is equal to 50º.
Explanation:
Given: ∠OAB = 40º
Now, in triangle OAB,
OA = OB ...[Radii of circle]
So, ∠OAB = ∠OBA = 40º ...[Angle opposite to equal sides are equal]
So, ∠AOB = 180º – (40º + 40º) = 100º
As we know that angle subtended by an arc of a circle at the center is double the angle subtended by it at any point on the remaining part of the circle.
So, ∠ACB = `1/2` ∠AOB = `1/2 xx 100^circ` = 50º
APPEARS IN
RELATED QUESTIONS
In the fig. a circle is inscribed in a quadrilateral ABCD in which ∠B = 90° if AD = 23cm,
AB = 29cm and DS = 5cm, find the radius of the circle.
In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.
In Fig. 4, a circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.
In the given figure, two tangents AB and AC are drawn to a circle with centre O such that ∠BAC = 120°. Prove that OA = 2AB.
Use the figure given below to fill in the blank:
R is the _______ of the circle.
State, if the following statement is true or false:
The longest chord of a circle is its diameter.
If d1, d2 (d2 > d1) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, then ______
If a number of circles pass through the endpoints P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.
The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA = 110°, find ∠CBA see figure
In the following figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to ______.
