Question

ⓘⓕ ⓣⓦⓞ ⓔⓠⓤⓐⓛ ⓒⓗⓞⓡⓓ ⓞⓕ ⓐ ⓒⓘⓡⓒⓛⓔ ⓘⓝⓣⓔⓡⓢⓔⓒⓣ ⓦⓘⓣⓗⓘⓝ ⓣⓗⓔ ⓒⓘⓡⓒⓛⓔ , ⓟⓡⓞⓥⓔ ⓣⓗⓐⓣ ⓣⓗⓔ ⓢⓔⓖⓜⓔⓝⓣⓢ ⓞⓕ ⓞⓝⓔ ⓒⓗⓞⓡⓓ ⓐⓡⓔ ⓔⓠⓤⓐⓛ ⓣⓞ ⓒⓞⓡⓡⓔⓢⓟⓞⓝⓓⓘⓝⓖ ⓢⓔⓖⓜⓔⓝⓣ ⓞⓕ ⓞⓣⓗⓔⓡ ⓒⓗⓞⓡⓓ.

♠♠ⓝⓞⓝⓢⓔⓝⓢⓔ ⓐⓝⓢ ⓦⓘⓛⓛ ⓑⓔ ⓡⓔⓟⓞⓡⓣⓔⓓ♠♠

Answer 1

HY MATE


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If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Let PQ and RS be two equal chords of a given circle and they are intersecting each other at point T.


Draw perpendiculars OV and OU on these chords.
In ΔOVT and ΔOUT,
OV = OU (Equal chords of a circle are equidistant from the centre)
∠OVT = ∠OUT (Each 90°)
OT = OT (Common)
∴ ΔOVT ≅ ΔOUT (RHS congruence rule)
∴ VT = UT (By CPCT) ... (1)
It is given that,
PQ = RS ... (2)
⇒
⇒ PV = RU ... (3)
On adding equations (1) and (3), we obtain
PV + VT = RU + UT
⇒ PT = RT ... (4)
On subtracting equation (4) from equation (2), we obtain
PQ − PT = RS − RT
⇒ QT = ST ... (5)
Equations (4) and (5) indicate that the corresponding segments of chords PQ and RS are congruent to each other.




Hope helped you

Answer 2

Answer:Given; circle with centre O in which chords AB and CD intersect at M.
To Prove: AM = DM and CM = BM

In ΔAOM and ΔDOM
OA = OD (radii)
OM = OM (common side)
So, ΔAOM ≈ Δ DOM
Hence, AM = DM proved
It is given that AB = CD
So, AB – AM = CD – DM
Or, CM = BM proved