Mathematics
In the figure (ii) given below, two circles with centres C, C' intersect at A, B and the point C lies on the circle with C'. PQ is a tangent to the circle with centre C' at A. Prove that AC bisects ∠PAB.
Circles
36 Likes
Answer
In △ACB,
AC = BC (Radius of the same circle)
∴ ∠BAC = ∠ABC ….(i)
PAQ is tangent and AC is the chord of the circle.
∠PAC = ∠ABC (∵ angles in alternate segment are equal) ….(i)
From (i) and (ii)
∠BAC = ∠PAC
Hence, proved that AC bisects ∠PAB.
Answered By
24 Likes
Related Questions
If the sides of a rectangle touch a circle, prove that the rectangle is a square.
In the figure (i) given below, two circles intersect at A, B. From a point P on one of these circles, two line segments PAC and PBD are drawn, intersecting the other circles at C and D respectively. Prove that CD is parallel to the tangent at P.
In the figure (ii) given below, O and O' are centres of two circles touching each other externally at the point P. The common tangent at P meets a direct common tangent AB at M. Prove that,
(i) M bisects AB.
(ii) ∠APB = 90°.
In the figure (i) given below, AB is a chord of the circle with centre O, BT is tangent to the circle. If ∠OAB = 32°, find the values of x and y.
