Question

Please help with this question, thank you!!​

Answer 1

∵AB⊥XY ∴BX=BY
∵XY=3cm ∴BX= ½XY=1.5cm
Let the radius be r cm.
then, OX=OY=OA=r cm
∵AB=3.5cm ∴OB=3.5cm-r cm
∵AB⊥XY ∴OB²+BX²=OX²
∴(3.5-r)²+1.5²=r² ∴r=29/14
So the answer is 29/14 (2.1).

Answer 2

2.1 cm (nearest tenth)

Explanation:

The radius (r) of a circle is the distance between its center and its circumference. Therefore, from inspection of the given circle:

⇒ r = OX = OY = OA

Given:

• AB = 3.5 cm
• OA = r

⇒ AB = OA + OB

⇒ 3.5 = r + OB

⇒ OB = 3.5 - r

As OX = OY and AB is perpendicular to XY then XB = BY.

As XY = 3 cm:

⇒ XB = BY = 1.5 cm

Therefore, for ΔOBX:

• Leg a = OB = (3.5 - r) cm
• Leg b = XB = 1.5 cm
• Hypotenuse = OX = r cm

Pythagoras Theorem

`a^2+b^2=c^2`

where:

• a and b are the legs of the right triangle.
• c is the hypotenuse (longest side) of the right triangle.

Use Pythagoras Theorem and the defined sides of ΔOBX to find r:

`\implies OB^2+XB^2=OX^2`

`\implies (3.5-r)^2+1.5^2=r^2`

`\implies 12.25-7r+r^2+2.25=r^2`

`\implies 14.5-7r+r^2=r^2`

`\implies 14.5-7r+r^2-r^2=r^2-r^2`

`\implies 14.5-7r=0`

`\implies 14.5=7r`

`\implies 7r=14.5`

`\implies (7r)/(7)=(14.5)/(7)`

`\implies r=2.07142857...\: \sf cm`

Therefore, the radius of the circle is 2.1 cm (nearest tenth).