Theorem of Equal Angles Subtended by Different Chords

Q.

If the two chords in a circle are equal, then the angle it subtends at the centre is same.

1. False

2. True

Q.

Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB=\angle OAC.$ . Write True or False and justify your answer

Q. in the figure BD is the angle bisector of angle B in triangle ABC, point E is on AB and CE intersects BD at P. Quadrilateral BCDE is ccyclic.If BP=15cm and PE=5 cm and AE/AC=m/n, where m and n are in lowest form then find m+n.

Q.

Two poles of height ‘a’ metres and ‘b’ metres are ‘p’ metres apart. Prove that the height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by ab/(a+b) meters.

Q. 9. Find the number of degrees subtended at the centre of a circle by an Arc whose length is 0.357 times the radius

Q.

If the two chords in a circle are equal, then the angle it subtends at the centre is the same.

1. True

2. False

Q. If the two chords in a circle are equal, then prove that the angle it subtends at the centre is the same.

Q.

In the figure, $AC=10cm,PC=15cm,PQ=12cm,$ find PB.

1. $9cm$

2. $7cm$

3. $6cm$

4. $8cm$

Q. A quadrilateral ABC is drawn to circumscribe circle. Prove that AB + CD=AD+BC

Q. Find the measure of XY, if XY=12cm.

1. 6cm
2. 12cm
3. 10cm
4. 8cm

Q. Find $\angle ABC$ = ?
$\left[3Marks\right]$

Q. Two chords $AB$ and $CD$ of a circle are each at distance of $4$ cm from the centre. Then $AB$ = $CD$.

1. True
2. False
3. Cannot be decided
4. None of the above

Q. Question 2
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Q.

If the angles subtended by two chords of a circle at the centre are equal, then the lengths of the chords are unequal.

1. True

2. False