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Equal Intercept Theorem

In a triangle...

Question

In a triangle ABC, M and P are points on AB and N and Q are points on AC such that, MN || PQ || BC and AM = MP = PB. If AN = 2 cm, then NC = .

2 cm

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4 cm

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6 cm

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Solution

The correct option is B 4 cm

In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Then we can say that AN = NQ = QC. [ $∵$ By BPT Theorem]
Given, AN = 2 cm
$\Rightarrow$ NQ = QC = 2cm

Now, NC = NQ + QC
$\Rightarrow$ NC = 2 + 2 = 4 cm

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Similar questions

In a triangle ABC, P and Q are points on side AB and AC respectively,such that PQ is parallel to BC.If AP=2.4 cm, AQ=2cm, QC=3cm and BC=6cm, find AB and PQ.

Q. A triangle

A B C

in which

A B = A C,

M

is a point on

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and

N

is a point on

A C

such that if

B M = C N

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A M = A N .

Q. In a

△ A B C, P

and

Q

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A B

and

A C

respectively, such that

P Q ∥ B C

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A P = 2.4 c m, A Q = 2 c m, Q C = 3 c m

and

B C = 6 c m

, find

A B

and

P Q .

Q. In a

△ A B C, P

and

Q

are the points on sides

A B

and

B C

respectively, such that

P Q ∥ B C

. Also,

A P = 2 c m, P B = 4 c m, A Q = 3 c m

and

Q C = 6 c m

then find

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P and Q are points on the sides AB and AC respectively of a $Δ A B C$ . If AP = 2 cm, PB = 4 cm, AQ = 3 cm, and QC = 6 cm, show that BC = 3PQ.

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In a triangle ABC, M and P are points on AB and N and Q are points on AC such that, MN || PQ || BC and AM = MP = PB. If AN = 2 cm, then NC = .

The correct option is B 4 cm In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Then we can say that AN = NQ = QC. [ ∵ By BPT Theorem] Given, AN = 2 cm ⇒ NQ = QC = 2cm Now, NC = NQ + QC ⇒ NC = 2 + 2 = 4 cm

The correct option is B 4 cm

In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Then we can say that AN = NQ = QC. [ $∵$ By BPT Theorem]
Given, AN = 2 cm
$\Rightarrow$ NQ = QC = 2cm

Now, NC = NQ + QC
$\Rightarrow$ NC = 2 + 2 = 4 cm