In triangle ABC, bisectors of angle B and angle C meet each other at point P. Line AP when extended, cuts the side BC at Q. Then AP/PQ

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Q. In

△ A B C

, the bisector of

∠ B

meets AC at D. A line PQ||AC meets AB,BC and BD at P,Q and R respectively. Show that
(i)

P R . B Q = Q R . B P

(ii)

A B \times C Q = B C \times A P

State true or false:

Triangle

A B C

is similar to triangle

P Q R

. If bisector of

∠ B A C

meets

B C

at point

D

and the bisector of

∠ Q P R

meets

Q R

at point

M

, Then,

\frac{A B}{P Q} = \frac{A C}{P M} .

Q. In a triangle ABC, AB = 3, BC = 5 and AC =7. AP and CP are internal angle bisectors meeting at P. The square of length of AP is

Triangle ABC is similar to triangle PQR. The bisector of angle BAC meets BC at point D and the bisector of angle QPR meets QR at point M. Which of the following is correct?

$△ A B C$ and $△ D B C$ are two isosceles triangles on the same base $B C$ (see in fig.) If $A D$ is extended to intersect $B C$ at $P$ , show that
(i) $△ A B D ≅ △ A C D$
(ii) $△ A B P ≅ △ A C P$
(iii) $A P$ bisects $∠ A$ as well as $∠ D$ .
(iv) $A P$ is the perpendicular bisector of $B C$ .

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