In Fig. 10.10, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°. Is the given statement true or false and justify your answer
Solution:
Let us join CA and CB
ADCB is a cyclic quadrilateral
We know that, the sum of opposite angles will be 180°
∠ADC + ∠CBA = 180°
It is given that
∠ADC = 120°
∠CAB = 30°
Substituting the values
120° + ∠CBA = 180°
∠CBA = 180° - 120° = 60°
In triangle ACB
∠ACB = 90° (Angle subtended by the diameter of a circle to its centre is 90°)
∠CAB + ∠CBA + ∠ACB = 180°
Using the angle sum property of a triangle
∠CAB + 60° + 90° = 180°
By further calculation
∠CAB = 180° - 150° = 30°
Therefore, the statement is true.
✦ Try This: If A, B, C and D are four points such that ∠BAC = 40° and ∠BDC = 50°, then A, B, C, D are concyclic.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10
NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 10
In Fig. 10.10, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°. Is the given statement true or false and justify your answer
Summary:
The statement “In Fig. 10.10, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°” is true
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