Question

missing number
42
43
95
50
?​

Answer 1

Answer:

Given, AP = 10 cm and ∠APB = 60° Represented in the figure We know that, A line drawn from centre to point from where external tangents are drawn divides or bisects the angle made by tangents at that point So, ∠APO = ∠OPB = 1/2 × 60° = 30° And, the chord AB will be bisected perpendicularly ∴ AB = 2AM In ∆AMP, AM = AP sin 30° AP/2 = 10/2 = 5cm [As AB = 2AM] So, AP = 2 AM = 10 cm And, AB = 2 AM = 10 cm Alternate method: In ∆AMP, ∠AMP = 90°, ∠APM = 30° ∠AMP + ∠APM + ∠MAP = 180° 90° + 30° + ∠MAP = 180° ∠MAP = 60° In ∆PAB, ∠MAP = ∠BAP = 60°, ∠APB = 60° We also get, ∠PBA = 60° ∴ ∆PAB is equilateral triangle AB = AP = 10 cmRead more on Sarthaks.com - https://www.sarthaks.com/656091/if-and-are-tangents-from-outside-point-such-that-pa-10-cm-and-apb-60-find-the-length-of-chord