Question

1. AB is tangent to circle O at B. The diagram is not drawn to scale. . . circle O. . If AB = 9 and AO = 21.6, what is the length of the radius (r)? Round the answer to the nearest tenth. A. 19.6. B.15.3*. C.23.4. D.12.6. 2. JK, KL, and LJ are all tangent to circle O. The diagram is not drawn to scale. . . triangle JLK with an inside circle O. . If JA = 12, AL = 15, and CK = 5, what is the perimeter of ΔJKL? (1 point). 34. 64 *. 32. 54. 3. WZ and XR are diameters of circle C. The diagram is not drawn to scale. . . . . What is the measure of ____ A. 355º. B.5º. C. 292º. D.243º.

Answer 1

1) The correct answer is A) 19.6

See the first picture attached.

A line tangent with a circle (AB) forms a 90° angle with the radius drawn from the tangent point (BO). This means that you can apply the Pythagorean theorem:
BO = √(AO² - AB²)
= √(21.6² - 9²)
= √(466.56 - 81)
= √385.56
= 19.6

2) The correct answer is B) 64

See the second picture attached.

When you have an incircle (a circle inscribed in a triangle), the distances between a vertex and the two nearest tangent points are equal to each other.

This means that:
JA = JB
LA = LC
KC = KB

Therefore the perimeter of ΔJKL will be:
2 × (12 + 15 + 5) = 64

3) The question asks for the measure of arc ZWX
The correct answer is D) 243°

See the third picture attached.

We know that a diameter forms an arc of 180°, because it divides the circle into two equal parts.

Therefore, arc ZRW measures 180°.

In order to find arc ZWX you need to add arc ZRW and arc WX:
ZWX = ZRW + WX
= 180 + 63
= 243°