Challenges on Properties of Equal Chords and Distances of Chords from the Center

Q. Type of congruency of $△OAB$ and $△OCD$ is

1. Side Angle Side
2. Angle Side Angle
3. Angle Angle Side
4. Side Side Side

Q. The chords AC and ZX are of same length. P is the center of the circle of radius 10 units. If ZY = 6 units, the length of PB is units.

Q. Find the area of the right triangle whose one side passes through the center of the circle having a radius of $5\text{units}$ and base of the triangle lies on a chord of length $8\text{cm}$.

1. $8{\text{unit}}^2$
2. $16{\text{unit}}^2$

Q. If $PB=PY$ for the circle with center at $P,$ find the possible pairs of $(x,y).$

1. $(1,9)$
2. $(0,6)$
3. $(-1,3)$

Q. If $\text{OM}=\text{ON}=4$ units, $\text{OP}=5$ units, then $\text{PQ}$ and $\text{RS}$ will be

1. $8$ units, $8$ units
2. $6$ units, $6$ units
3. $5$ units, $8$ units
4. $6$ units, $5$ units