Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 9.27). Prove that ∠ACP = ∠ QCD
Join chords∠ AP and ∠DQ.
For chord AP,
∠PBA=∠ACP (Angles in the same segment) .... (1)
For chord DQ,
∠DBQ=∠QCD (Angles in the same segment) …. (2)
ABD and PBQ are line segments intersecting at B.
∠PBA=∠DBQ (Vertically opposite angles) .... (3)
From equations (1), (2), and (3), we obtain
∠ACP=∠QCD
In Fig. 9.23, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
In Fig. 9.26, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.
In Fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.
A driver of a car travelling at \(52\) \(km \;h^{–1}\) applies the brakes Shade the area on the graph that represents the distance travelled by the car during the period.
Which part of the graph represents uniform motion of the car?