Question

Can someone please help me with these questions.

1. what is the value of x in the circle below?
x=19
x=13.6
x=20.5
x=23.4

2.what is the value of x in the circle below?
x=114
x=33
x=57
x=16.5

3.WZ and XR are diameters. what is the measure of ZWX?
214
266
60
300

4. if the measurement of R=31,what is the measurement of O?
31
59
62
149

Answer 1

Answer 1) 13.6cm
Answer 2)33°
Answer 3)how can someone find the measure of zwx. I think your question is wrong. or you have typed the question wrongly.

Answer 4)r is radius or RQ or RN.

Answer 2

1).

Given length of chord, AB = 22 unit

length of perpendicular OC = 8 unit

Perpendicular from center bisect the chord.

⇒ AC = BC = 11 unit

In Δ AOC

by Pythagoras theorem,

OA² = OC² + AC²

OA² = 8² + 11²

OA² = 64 + 121

OA² = 185

OA = √185

OA = 13.6

x = OA = 13.6 unit

Therefore, option 2 is correct.i.e, x = 13.6

2).

Given: CD = AB

Equal chords substend equal angles at centre.

using this result , we get

⇒ x = 33°

Therefore, Option 2 is correct.i.e., x = 33°

3).

In Δ CWX

CW = CX ( radius of circle )

By using result which says that angles oppsoite to equal sides are equal

⇒ ∠CWX = ∠CXW

⇒ ∠CWX + ∠CXW + ∠WCX = 180° ( Angle sum property )

⇒ 2 × ∠CWX = 180 - 34

∠CWX = $\frac{146}{2}$

∠CWX = 73°

⇒ ∠ZWX = ∠CWX = 73°

4).

Given: ∠ R = 31°

To Find: ∠ O  

Angle subtended by chord on center is double of angle subtended at corresponding major arc.

Using this result we get,

⇒ ∠O = 62°

Therefore, Option 3 is correct.i.e, ∠O = 62°