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Theorem of Equal Angles Subtended by Different Chords

in the given ...

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in the given figure, P,Q and R are the mid-points of sides AB. AC and BC of triangle ABC respectuely IF AD is perpendicular to BC. then prove that PQRD is a cyclic quadrlateral.

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Q. In the quadrilateral given below,

A D = B C . P, Q, R

S

are mid-points of

A B, B D, C D

A C

respectively. Prove that

P Q R S

Q. Given an equilateral triangle ABC, D, E, and F are the mid-points of the sides AB, BC, and AC, respectively, then the quadrilateral BEFD is exactly a

B C, C A

A B

A B C

a, b, c

respectively. If

D

is the mid-point of

B C

A D

is perpendicular to

A C

then the value of

cos A cos C

Q. Question 5
P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC = BD and

A C ⊥ B D

. Prove that PQRS is a square.

□ A B C D

is a quadrilateral

P, Q, R, S

are the mid point of side

A B, B C, C D, A C

respectively. Prove that

□ P Q R S

is a parallelogram.

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Theorem of Equal Angles Subtended by Different Chords

Standard IX Mathematics

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