Question

ASAP

Given: △ABC, BK=10, AC=30, m∠NMO=90°, MN = MO,
BK⊥AC, NO∥AC, M∈AC

FIND: NO

Answer 1

Answer:

Step-by-step explanation:

I have a slightly different way to solve this.

Let P be the mid-point of NO.

As MN = MO, MNO is an isosceles triangle,

line MP is ⊥ to NO

As ∠NMO=90°, triangle MNO is similar to triangles PNM and POM.

MP = NP = PO

MP = NO/2

Let Q be the interaction of BK and NO

BQ = BK - QK

As QK = MP

BQ = BK - MP

= 10 - NO/2

Triangle BNO and BAC are similar

BQ/NO = BK/AC

Substituting BQ by 10 - NO/2

(10 - NO/2) / NO = 10 /30

NO = 3*(10 - NO/2)

NO = 30 - 3*NO/2

5*NO/2 = 30

NO = 12

Answer 2

The value of NO is 12 if the : △ABC, BK=10, AC=30, m∠NMO=90°, MN = MO, BK⊥AC, NO∥AC, M∈AC

What is the triangle?

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

Draw MP a line upto line NO touches on point P and

MP ⊥ NO

P is a mid-point of NO

MN = MO (given)

∠NMO=90° (given)

Triangle MNO  ~ triangles PNM and POM.

MP = NP = PO

MP = NO/2

Let's suppose Q is the interaction of BK and NO

BQ = BK - QK

QK = MP (from the figure)

BQ = BK - MP  (∵QK = MP)

BQ  = 10 - NO/2 (MP = NO/2)

Triangle BNO and BAC are similar

BQ/NO = BK/AC

(10 - NO/2) / NO = 10 /30

After solving, we get:

NO = 12

Thus, the value of NO is 12 if the : △ABC, BK=10, AC=30, m∠NMO=90°, MN = MO, BK⊥AC, NO∥AC, M∈AC

Learn more about the triangle here:

brainly.com/question/25813512

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