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 given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 60° then find the measure of ∠OAB.
In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.
In the given figure, ABCD is a cyclic quadrilateral. If ∠BCD = 100° and ∠ABD = 70°, find ∠ADB.
If ABCD is a cyclic quadrilateral in which AD || BC (In the given figure). Prove that ∠B = ∠C.
Find the area of the shaded region in the figure If ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. (Take π= 3.14)
The longest chord of a circle is __________
Twice the radius is ________________
The circumcentre of the triangle ABC is O. Prove that ∠OBC + ∠BAC = 90º.
Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how much accurate is your estimate.
A circle of radius 3 cm with centre O and a point L outside the circle is drawn, such that OL = 7 cm. From the point L, construct a pair of tangents to the circle. Justify LM and LN are the two tangents.
