Mathematics
In the figure (ii) given below, it is given that ∠ABC = 40° and AD is a diameter of the circle. Calculate ∠DAC.
Answer
Consider △ABC and △ADC,
∠ABC = ∠ADC = 40° (∵ angles in same segment are equal.)
In △ADC,
∠DCA = 90° (∵ angle in semicircle is 90°.)
We know that sum of angles of a triangle is 180°.
⇒ ∠DAC + ∠ADC + ∠DCA = 180°.
⇒ ∠DAC + 40° + 90° = 180°
⇒ ∠DAC + 130° = 180°
⇒ ∠DAC = 180° - 130°
⇒ ∠DAC = 50°.
Hence, the value of ∠DAC = 50°.
Related Questions
In the figure (i) given below, AB is a diameter of the circle APBR. APQ and RBQ are straight lines, ∠A = 35°, ∠Q = 25°. Find :
(i) ∠PRB
(ii) ∠PBR
(iii) ∠BPR
In the figure (ii) given below, AB is a diameter of the circle whose center is O. Given that ∠ECD = ∠EDC = 32°, calculate
(i) ∠CEF
(ii) ∠COF
In the figure (i) given below, P and Q are centers of two circles intersecting at B and C. ACD is a straight line. Calculate the value of x.
In the figure (ii) given below, O is the circumcenter of triangle ABC in which AC = BC. Given that ∠ACB = 56°, calculate
(i) ∠CAB
(ii) ∠OAC.
