2) Given : chord AB = chord BC =
chord AC, ZBAP = ZCAP.
To prove : Seg CB = seg CQ.
Answers
If chord AB = chord BC = chord AC, ∠BAP = ∠CAP, then Segment CB = segment CQ is proved.
Step-by-step explanation:
Since it is given, chord AB = chord BC = chord AC
∴ ∆ ABC will be an equilateral triangle so ∠CAB = ∠ABC = ∠ACB = 60°
Also given, ∠BAP = ∠CAP = ½ * ∠CAB = 30°
From the figure we get
∠ACB + ∠BCQ = 180° …… [∵ Linear pair]
⇒ 60° + ∠BCQ = 180°
⇒ ∠BCQ = 180° - 60°
⇒ ∠BCQ = 120°
We know that an angle formed by the two secants is one half of the difference of its intercepted arcs.
Therefore, we can say
∠AQB = ½ * [arcAB – arcCP] = ½ * [120° - 60°] = ½ * 60° = 30°
Now, consider ∆CBQ, applying angle sum property, we get
∠AQB + ∠CBQ + ∠BCQ = 180°
⇒ 30° + ∠CBQ + 120° = 180°
⇒ ∠CBQ = 180° - (120° + 30°)
⇒ ∠CBQ = 30°
Since in ∆CBQ, ∠CBQ = ∠AQB = 30°
∴ ∆CBQ is an isosceles triangle
⇒ segment CB = segment CQ
Hence proved
----------------------------------------------------------------------------------------
Also View:
If two arcs of circle are congruent then corresponding chords are equal.
https://brainly.in/question/7393424
If arcs AXB and CYD of a circle are congruent,find the ratio of chord AB and chord CD .
https://brainly.in/question/1200059
The radius of a circle is 30 cm. find the length of an arc ,if the length of the chord of the arc is 30 cm .
https://brainly.in/question/3347563
