Mathematics
In the given figure, A, C, B, D are points on the circle with centre O. Given ∠ABC = 62°. Find :
(i) ∠ADC
(ii) ∠CAB
Answer
(i) From figure,
⇒ ∠ADC = ∠ABC (Angles in same segment are equal)
⇒ ∠ADC = 62°.
Hence, ∠ADC = 62°.
(ii) We know that,
Angle in a semi-circle is a right angle.
∠ACB = 90°
Using angle sum property,
⇒ ∠CAB + ∠ACB + ∠ABC = 180°
⇒ ∠CAB + 90° + 62° = 180°
⇒ ∠CAB + 152° = 180°
⇒ ∠CAB = 180° - 152°
⇒ ∠CAB = 28°.
Hence, ∠CAB = 28°.
Related Questions
In the given figure, ABCDE is a pentagon inscribed in a circle such that AC is a diameter and side BC ∥ AE. If ∠BAC = 50°, find giving reasons :
(i) ∠ACB
(ii) ∠EDC
(iii) ∠BEC
Hence prove that BE is also a diameter.
In the given figure, O is the centre of the circle and AB is a diameter. If AC = BD and ∠AOC = 72°, find:
(i) ∠ABC
(ii) ∠BAD
(iii) ∠ABD
The angle in a semi-circle is :
an acute angle
an obtuse angle
a right angle
can be either acute or obtuse
The angle subtended by an arc of a circle at any point on the remaining part of the circle is of the angle subtended by it at the centre.
double
half
equal
triple