AB and CD are two chords in a circle with centre O and AD is the diameter. When produced, AB and CD meet at the point P. If ∠DAP = 39°, ∠APD = 25°, then what is the measure (in degrees) of ∠DBC?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 26
AB and CD are two chords in a circle with center O and AD is a diameter.
AB and CD produced meet at a point P outside the circle.
∠APD = 250
∠DAP = 390
Exterior angle theorem -
An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles. The angle subtended from a diameter is 900. The opposite angles of a triangle are equal.
According to the question -
In ΔADP -
∠ADC = ∠DAP + ∠DPA
∠ADC = 250 + 390
∠ADC = 640
Angles in the same segment are equal.
∠ADC = ∠ABC = 640 ....(I
Since AD is a diameter.
So, ∠ABD = 900
∠ABC + ∠CBD = 900
640 + ∠CBD = 900 [From (i)]
∠CBD = 260