Question

AB and CD are two chords of circle with centre O . If ∠ = 75° and

∠ = 75° , find the length of CP , given that AB = 10cm and OP is

perpendicular to C​

Answer 1

Step-by-step explanation:

xbdndhfidrofiforjrj and I have done the same

Answer 2

Answer:

Even though the question is not clear, but with a basic understanding:

AB and CD are two chords.

( I am taking OR to be the perpendicular to AB since you haven't mentioned it )

Take OR and OP to be perpendiculars from the center drawn to the chords AB and CD respectively.

Triangle PRO is formed. It is given that angle OPR = angle ORP = 75 degrees.

Therefore, base angles are equal. Base angles are equal when opposite sides to the base angles are also equal. Thus, triangle PRO is isosceles.

Since the sides opposite to the base angles have to be equal as it is an isosceles triangle, OP = OR ( the two perpendiculars joining the center and the chord )

If the perpendiculars drawn are equal, then the chords they are perpendicular to are also equal. Therefore, AB = CD.

Thus, AB = CD = 10 cm

When a perpendicular from the center is drawn to a chord, the perpendicular bisects the chord.

Since OP is a perpendicular drawn from the center to the chord CD, OP will bisect CD.

Therefore, CP = PD

CP = 10/2 = 5cm

HOPE IT HELPS ;)