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Standard X

Mathematics

Basic Proportionality Theorem and Its Forms

BO and CO are...

Question

BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP ,

AB/AC = BP/PC , AP is the bisector of angle BAC.

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Q. In given figure BO and CO are respectively the bisectors of

∠ B

and

∠ C

△ A B C

. AO produced meets BC at P show that

(i)

\frac{A B}{B P} = \frac{A O}{O P}

(ii)

\frac{A C}{C P} = \frac{A O}{O P}

(iii)

\frac{A B}{A C} = \frac{B P}{P C}

(iv) AP is the bisector of

∠ B A C

BO and CO are respectively the bisectors of $∠ B$ and $∠ C$ of $Δ A B C$ . AO produced meets BC at P.

Show that [4 MARKS]

(i) $\frac{A B}{B P} = \frac{A O}{O P}$

(ii) $\frac{A C}{C P} = \frac{A O}{O P}$

(iii) $\frac{A B}{A C} = \frac{B P}{P C}$

(iv) $A P$ is the bisector of $∠ B A C$ .

Q. In a triangle ABC, AB = AC and the bisectors of angles B and C intersect at O. Prove that BO = CO and AO is the bisector of angle

∠ B A C

Q. In

△

ABC, AB=AC and the bisectors of angles B and C intersect at point O. Prove that BO = CO and the ray AO is the bisector of angle BAC.

Q. If

B O

and

C O

are respectively the fraction Of

∠ B

∠ C

△ A B C

A O

produced meets as at

P

and find the

A B / A C

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BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP , AB/AC = BP/PC , AP is the bisector of angle BAC.

We found a similar question to the one that you posted. Please check it out here.

BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP ,

AB/AC = BP/PC , AP is the bisector of angle BAC.