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
Prove that the tangents at the extremities of any chord make equal angles with the chord.
If ΔABC is isosceles with AB = AC and C (0, 2) is the in circle of the ΔABC touching BC at L, prove that L, bisects BC.
In the given figure, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that point of contact P bisects the base BC.
In the given figure, a circle with center O, is inscribed in a quadrilateral ABCD such that it touches the side BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm then find the radius of the circle.
In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60°, find ∠PRQ.
In the given figure, BDC is a tangent to the given circle at point D such that BD = 30 cm and CD = 7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right angle triangle. Calculate (i) AF
Find the diameter of the circle if the length of a chord is 3.2 cm and itd distance from the centre is 1.2 cm.
The longest chord of a circle is __________
Find the radius of the circle
Diameter = 30 cm
A line through the point of contact and passing through centre of the circle is known as ______
