Advertisements
Advertisements
Question
In the following figure, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
Let AOB be the diameter of the circle.
Given: ∠ADC = 120°
Firstly, join CB.
Then, we have a cyclic quadrilateral ABCD.
Since sum of opposite angles of cyclic quadrilateral is 180°, therefore
∠ADC + ∠ABC = 180°
⇒ 120° + ∠ABC = 180°
⇒ ∠ABC = 180° – 120°
⇒ ∠ABC = 60°
Now join AC.
Also, diameter subtends a right angle to the circle,
∴ In ΔABC, ∠ACB = 90°
Now, by angle sum property of a triangle, sum of all angles of a triangle is 180°.
∴ ∠CAB + ∠ABC + ∠ACB = 180°
⇒ ∠CAB + 60° + 90° = 180°
⇒ ∠CAB = 180° – 90° – 60°
⇒ ∠CAB = 30°
APPEARS IN
RELATED QUESTIONS
Write True or False. Give reason for your answer.
Sector is the region between the chord and its corresponding arc.
In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC
at P and OA at Q. Prove that:
(i) ΔOPA ≅ ΔOQC, (ii) ΔBPC ≅ ΔBQA.
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.
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.
Find the area of a circle of radius 7 cm.
If O is the centre of the circle, find the value of x in each of the following figures
In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords?
If the angle between two radii of a circle is 130°, then the angle between the tangents at the ends of the radii is ______
In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ______.
From the figure, identify a chord.
