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 blank
A continuous piece of a circle is ............... of the circle
A quadrilateral is drawn to circumscribe a circle. Prove that the sums of opposite sides are equal ?
If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
Use the figure given below to fill in the blank:
If PQ is 8 cm long, the length of RS = ________
Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).
| radius (r) | diameter (d) | Circumference (C) |
| 24 m |
In the figure, O is the centre of a circle, AB is a chord, and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to ______
In the following figure, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.
In the following figure, O is the centre of the circle. Name all radii of the circle.
Say true or false:
The centre of a circle is always in its interior.
A 7 m broad pathway goes around a circular park with a circumference of 352 m. Find the area of road.
