Mathematics
AB is diameter of the circle and ∠ACD = 38°.
Assertion (A) : x = 38°.
Reason (R) : ∠ACB = 90°, x = ∠DCB = 90° - 38° = 52°.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
Answer
Join DB and CB.
It is given AB is diameter of the circle and angles in a semicircle is a right angle.
⇒ ∠ACB = 90°
⇒ ∠ACD + ∠DCB = 90°
⇒ 38° + ∠DCB = 90°
⇒ ∠DCB = 90° - 38°
⇒ ∠DCB = 52°
We know that, angles subtended by the same chord in the same segment of a circle are equal.
⇒ ∠BAD (x) = ∠BCD = 52°
So, assertion (A) is false but reason (R) is true.
Hence, option 2 is the correct option.
Related Questions
ABCD is a cyclic quadrilateral, BD and AC are its diameters. Also, ∠DBC = 50°.
Assertion (A) : ∠BAC = 40°.
Reason (R) : ∠BAC = ∠BDC = 180° - (50° + 90°) = 40°.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
Points A, C, B and D are concyclic, AB is diameter and ∠ABC = 60°.
Assertion (A) : ∠BAC = 60°.
Reason (R) : AB is diameter so ∠ACB = 90° and ∠ABC + ∠BAC = 90°.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
A circle with center at point O and ∠AOC = 160°.
Statement (1) : Angle x = 100° and angle y = 80°.
Statement (2) : The angle, which an arc of a circle subtends at the center of the circle is double the angle which it subtends at any point on the remaining part of the circumference.
Both statements are true.
Both statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.