Question

what would be the answer ​

Answer 1

We have the values of AB and AD, so we can easily find the length of BD by applying Pythagoras' Theorem.

Thus,

BD = √[(AB)² + (AD)²]

BD = √(12² + 9²)

BD = √(144 + 81)

BD = √225

BD = 15 cm

In the semicircle, since AD is a diameter of the semicircle and the angle AXD is subtended by this diameter, then we have,

⟨AXD = 90°

So that AX is an altitude in ∆ABD drawn from A to BD.

Then, by the area of ∆ABD we get the following equation,

(AB · AD) / 2 = (AX · BD) / 2,

since AB is perpendicular to AD.

So,

AB · AD = AX · BD

12 · 9 = 15 · AX

AX = 7.2 cm

Then, by Pythagoras' Theorem,

BX = √[(AB)² - (AX)²]

BX = √[12² - (7.2)²]

BX = √(144 - 51.84)

BX = √92.16

BX = 9.6 cm

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