In circle J with mZHLK = 18, find the mZHJK.

The measure of angle HJK is 36°

Step-by-step explanation:

In a circle, the measure of the inscribed angle equal half the measure of the central angle subtended by the same arc

In circle J

∵ J is the center of the circle

∵ H and K lie on the circle

∴ ∠HJK is a central angle subtended by arc HK

∵ L lies on the circle

∴ ∠HLK is an inscribed angle subtended by arc HK

→ By using the rule above

∵ ∠HJK and ∠HLK are the central angle and inscribed angle

   subtended by the same arc HK

∴ m∠HLK = m∠HJK

∵ m∠HLK = 18°

∴ 18 = m∠HJK

→ Multiply both sides by 2

∴ 36 = m∠HJK

∴ The measure of angle HJK is 36°

Answer : The area of ΔABC is,

Step-by-step explanation :

Given:

Side AM = 48 inches

Side AC = 40 inches

Side BC = 100 inches

First we have to determine the side CM and side BM.

As, AM is a median of an acute triangle ABC. So, median divides the side BC into two equal side.

That means,

Side CM = Side BM = = 50 inches

Now we have to determine the semi-perimeter of ΔAMC.

Formula used :

Now we have to determine the area of ΔAMC.

Using Heron's formula:

where,

A is a area, s is a semi-perimeter and a, b, c are the sides of triangle.

Thus, the area of ΔAMC =

Now we have to determine the area of ΔABC.

As we know that, each median of a triangle divides the triangle into two smaller triangles which have equal area.

So,

ΔABC = 2 × ΔAMC

ΔABC =

ΔABC =

Thus, the area of ΔABC is,