In a circle with center O, AB is the diameter and CD is a chord such that ABCD is a trapezium. If ∠BAC = 18°, then ∠CAD is equal to:
Show answer & explanation
Correct answer: A
Explanation
Correct answer is option 1 i.e. 54°
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Concept |
Understanding |
Application |
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Angles subtended by same arc on the circumference of a circle are equal. |
Given, ∠BAC = 18° ⇒ ∠ACB = 90° [Angle in a semicircle is 90°] |
In ΔACB ⇒ ∠ACB + ∠CBA + ∠BAC = 180° ⇒ ∠CBA = 180° - 90° - 18° = 72° ⇒ ∠DCA = ∠CAB = 18° [Alternate interior angle] ⇒ ∠DCA = ∠ABD = 18° and ∠CAD = ∠DBC ⇒ ∠CBA = ∠DBC + ∠ABD ⇒ 72° = ∠DBC + 18° ⇒ ∠DBC = 72° - 18° = 54° ⇒ ∠CAD = ∠DBC = 54° |