Advertisements
Advertisements
Question
In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ______.
Options
30º
60º
90º
45º
Advertisements
Solution
In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to 45º.
Explanation:
We know that, diameter subtends a right angle to the circle.
∴ ∠BCA = 90º ...(i)
Given, AC = BC
⇒ ∠ABC = ∠CAB ...(ii) [Angles opposite to equal sides are equal]
In ΔABC, ∠CAB + ∠ABC + ∠BCA = 180º ...[By angle sum property of a triangle]
⇒ ∠CAB + ∠CAB + ∠90º = 180º ...[From equations (i) and (ii)]
⇒ 2∠CAB = 180º – 90º
⇒ ∠CAB = `(90^circ)/2`
∴ ∠CAB = 45º
APPEARS IN
RELATED QUESTIONS
Fill in the blanks:
A circle divides the plane, on which it lies, in __________ parts.
Fill in the blank
Circles having the same centre and different radii are called ...........................circles.
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the lengths of TP and TQ.
Find the length of the chord of a circle in the following when:
Radius is 1. 7cm and the distance from the centre is 1.5 cm
ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.
Use the figure given below to fill in the blank:
If PQ is 8 cm long, the length of RS = ________
The longest chord of a circle is __________
In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is ______
From the figure, identify the centre of the circle.
From the figure, identify a chord.
