Question

Pa and pb is tangent to circle o angle apb is 60 Find ab

Answer 1

[1]If PA and PB are tangents from an outside point P such that PA = 10 cm and angle APB = 60 .find the length of the chord AB.

[2]prove that the tangent drawn at the ends of a chord of a circle make equal with the chord.

[3]prove that the line segment joining the points of contact of two parallel tangent to a circle is a diameter of the circle.

Answer 2

Answer:

The answer is given below hope it help

Step-by-step explanation:

Given : PA and PB are tangents of a circle, PA = 10 cm and ∠APB = 60°

Let O be the center of the given circle and C be the point of intersection of OP and AB

In ΔPAC and ΔPBC

PA = PB(Tangents from an external point are equal)

∠APC = ∠BPC (Tangents from an external point are equally inclined to the segment joining center to that point)

PC = PC (Common)

Thus, ΔPAC is congruent to ΔPBC (By SAS congruency rule) ..........(1)

∴ AC = BC

Also ∠APB = ∠APC + ∠BPC

∠APC=1/2∠APB. {∠APC = ∠BPC}

1/2×60°=30°

∠ACP + ∠BCP = 180°. {∠ACP =∠BCP}

∠ACP=1/2×180°

Now in right triangle ACP

sin30°=AC/AP

1/2=AC/10

AC=10/2=5

∴ AB = AC + BC = AC + AC  (AC = BC)

⇒ AB = (5 + 5) cm = 10 cm

Hope it helped.....☺️