Q1. P is the centre of the circle. A tangent is drawn which touches the circle at M. If angle BPM = 70°, then what is the measure, in degrees, of angle DMR?
A 55° Correct
B 60°
C 70°
D 75°
Explanation
From the figure, B, P and D lie on one straight line through the centre, so angle DPM is 180° - 70° = 110°. Since PD and PM are radii of the same circle, triangle DPM is isosceles; each base angle at D and M is (180° - 110°)/2 = 35°. The tangent at M is perpendicular to the radius PM, so angle PMR is 90°. Therefore angle DMR is 90° - 35° = 55°. The other measures do not satisfy these radius, diameter and tangent relations.