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

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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

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

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

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions