$∠ B A C o f △ A B C$ is obtuse and AB = AC. P is a point in BC such that PC= 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively. If PQ = 15 cm and PR = 9 cm; find the length of PB.

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Solution

In $△$ ABC,

AC = AB [given]

⇒ $∠$ B = $∠$ C [angles opposite to equal sides are equal]

In $△$ PRC and $△$ PQB

$∠$ C = $∠$ B [Proved above]

$∠$ PRC = $∠$ PQB [90° each]

⇒ $△ P R C \sim △$ PQB [AA]

$fraction numerator P R over denominator P Q end fraction equals fraction numerator R C over denominator Q B end fraction equals fraction numerator P C over denominator P B end fraction fraction numerator P R over denominator P Q end fraction equals fraction numerator P C over denominator P B end fraction 9 over 15 equals fraction numerator 12 over denominator P B end fraction P B equals 20 space c m$

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Q. Hello,
Please help me with the following :
Angle BAC of triangle ABC is obtuse and AB=AC. P is a point in bc such that PC =12cm. PQ & PR are perpendicular to sides AB &AC respectively. If PQ=15cm and PR=9cm; find the length of PB.

regards,
Nikita

∠ B A C

of triangle

A B C

is obtuse and

A B = A C

P

is a point in

B C

such that

P C = 12

cm.

P Q

and

P R

are perpendiculars to sides

A B

and

A C

respectively. If

P Q = 15

cm and

= 9

cm; find the length of

P B

Angles BAC of triangle ABC is obtuse and AB = AC. P is a point in BC such that PC = 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively.

If PQ = 15 cm and PR = 9 cm; then the length of PB is ___ cm.

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively.

Prove that :
(i) PR = QR (ii) BQ = CP

In the given figure a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point of contact D are of length 9 cm and 3 cm respectively. Find the length of sides AB and AC.

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∠BAC of △ABC is obtuse and AB = AC. P is a point in BC such that PC= 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively. If PQ = 15 cm and PR = 9 cm; find the length of PB.

In △ ABC, AC = AB [given] ⇒∠ B = ∠ C [angles opposite to equal sides are equal] In △PRC and △PQB ∠ C = ∠ B [Proved above] ∠ PRC = ∠ PQB [90° each] ⇒△PRC∼△ PQB [AA]

$∠ B A C o f △ A B C$ is obtuse and AB = AC. P is a point in BC such that PC= 12 cm. PQ and PR are perpendiculars to sides AB and AC respectively. If PQ = 15 cm and PR = 9 cm; find the length of PB.